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GED Math : Squares, Rectangles, and Parallelograms

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Example Question #301 :Geometry And Graphs

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in brown). The dirt path is six feet wide throughout. Which of the following polynomials gives the perimeter of thegarden, in feet?

Possible Answers:

3x-24

6x-48

6x-24

3x-48

Correct answer:

6x-48

Explanation:

The length of the garden, in feet, is $2 \times 6 = 12$ feet less than that of the entire lot, or

L = 2x-12 ．

The width of the garden, in feet, is $2 \times 6 = 12$ less than that of the entire lot, or

W = x-12 ．

The perimeter, in feet, is twice the sum of the two:

P = 2 (L + W)

= 2 (2x-12 + x - 12 )= 2 (3x-24) = 6x - 48

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Example Question #302 :Geometry And Graphs

Given Square ABCD , the distance fromtois one mile. Which of the following gives the perimeter of the square, to the nearest foot?

Possible Answers:

$7,467\textrm{ ft}$

$29,868\textrm{ ft}$

$10,560\textup{ ft}$

$14,934\textrm{ ft}$

Correct answer:

$14,934\textrm{ ft}$

Explanation:

The segment $\overline{AC}$ is a diagonal of the square. It is also the hypotenuse of a right triangle whose legs both measure the same length, which we will call; this is also the length of one side of the square.

The right triangle formed is an isosceles triangle - and, subsequently, a $45^{\circ }-45^{\circ }-90^{\circ }$ triangle - and therefore,

$s \sqrt{2} = AC$

$\overline{AC}$ is one mile, or 5,280 feet, long, so we substitute AC = 5,280 and solve for:

$s \sqrt{2} = 5,280$

$s = 5,280 \div \sqrt{2} \approx 5,280 \div 1.414 \approx 3,733.5$

The perimeter, in feet, is four times this, or

$P = 4s \approx 4 \times 3,733.5 \approx 14,934$ feet.

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Example Question #303 :Geometry And Graphs

The length of each side of a square is increased by 12%. By what percent has its perimeter increased?

Possible Answers:

$44 \%$

$48 \%$

$12 \%$

$24 \%$

Correct answer:

$12 \%$

Explanation:

Letbe the original sidelength of the square. Increasing this by 12% is the same as adding 0.12 times that sidelength to the original sidelength. The new sidelength is therefore

s + 0.12s = 1.12s ．

The perimeter of a square is four times its sidelength. Its original perimeter was; after the increase, it is $4 \cdot 1.12s = 4.48 s$ ．The percent of increase is therefore

$\frac{4.48s - 4s }{4s} \times 100 \% = \frac{0.48 s}{4s} \times 100 \% = 0.12 \times 100 \% = 12 \%$ ．

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Example Question #304 :Geometry And Graphs

The perimeter of a square is 24cm. Find the length of one side of the square.

Possible Answers:

$7\text{cm}$

$3\text{cm}$

$\text{There is not enough information to answer the question.}$

$4\text{cm}$

$6\text{cm}$

Correct answer:

$6\text{cm}$

Explanation:

The formula to find the perimeter of a square is

P = 4a

whereais the length of any side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of one side of the square, we will solve fora．

Now, we know the perimeter of the square is 24cm. So, we will substitute and solve fora．We get

$24\text{cm} = 4a$

$\frac{24\text{cm}}{4} = \frac{4a}{4}$

$6\text{cm} = a$

$a = 6\text{cm}$

因此,广场的一边的长度6cm.

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Example Question #305 :Geometry And Graphs

Find the perimeter of a rectangle with a width of 8in and a length that is two times the width.

Possible Answers:

$16\text{in}$

$64\text{in}$

$36\text{in}$

$48\text{in}$

$24\text{in}$

Correct answer:

$48\text{in}$

Explanation:

找周长of a rectangle, we will use the following formula:

P = 2l + 2w

Wherelis the length andwis the width of the rectangle.

Now, we know the width of the rectangle is 8in. We also know the length is two times the width. Therefore, the length is 16in. So, we can substitute. We get

$P = 2(16\text{in}) + 2(8\text{in})$

$P = 32\text{in} + 16\text{in}$

$P = 48\text{in}$

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Example Question #306 :Geometry And Graphs

Find the perimeter of a square with a length of 8cm.

Possible Answers:

$48\text{cm}$

$64\text{cm}$

$16\text{cm}$

$24\text{cm}$

$32\text{cm}$

Correct answer:

$32\text{cm}$

Explanation:

找周长of a square, we will use the following formula:

P = 4a

whereais the length of one side of the square. Because a square has 4 equal sides, we can use any side in the formula.

Now, we know the length of the square is 8cm. So, we can substitute. We get

$P = 4 \cdot 8\text{cm}$

$P = 32\text{cm}$

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例子问题# 307:Geometry And Graphs

The perimeter of a square is 72in. Find the length of one side.

Possible Answers:

$9\text{in}$

$36\text{in}$

$18\text{in}$

$54\text{in}$

$16\text{in}$

Correct answer:

$18\text{in}$

Explanation:

To answer this, we will look at the formula for perimeter of a square. We get

P = 4a

whereais the length of one side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of one side, we will solve fora．Now, we know the perimeter of the square is 72\text{in}. So, we will substitute and solve fora．We get

$72\text{in} = 4a$

$\frac{72\text{in}}{4} = \frac{4a}{4}$

$18\text{in} = a$

$a = 18\text{in}$

因此,广场的一边的长度18in.

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Example Question #308 :Geometry And Graphs

The area of a square is $25\text{cm}^2$ ．Find the perimeter.

Possible Answers:

$5\text{cm}$

$\text{There is not enough information to solve the problem.}$

$25\text{cm}$

$30\text{cm}$

$20\text{cm}$

Correct answer:

$20\text{cm}$

Explanation:

正方形有4个等边。找周长of the square, we first have to find the length of one side of the square.

Now, we know the area of the square. The formula for area of a square is

A = b^2

wherebis the length of one side of the square. To find the length of one side, we will solve forb．Now, we know the area is $25\text{cm}^2$ ．So, we will substitute and solve forb.

$25\text{cm}^2 = b^2$

$\sqrt{25\text{cm}^2} = \sqrt{b^2}$

$5\text{cm} = b$

$b = 5\text{cm}$

因此,广场的一边的长度5cm.

Now, to find the perimeter of a square, we will use the following formula:

P = 4b

wherebis the length of one side of the square. Now, we know the length of one side of the square is 5cm. So, we can substitute. We get

$P = 4 \cdot 5\text{cm}$

$P = 20\text{cm}$

Therefore, the perimeter of the square is 20cm.

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Example Question #309 :Geometry And Graphs

Find the perimeter of a rectangle with a length of 9in and a width that is a third of the length.

Possible Answers:

$15\text{in}$

$18\text{in}$

$12\text{in}$

$24\text{in}$

$27\text{in}$

Correct answer:

$24\text{in}$

Explanation:

找周长of a rectangle, we will use the following formula:

P = 2l + 2w

wherelis the length andwis the width of the rectangle.

Now, we know the length of the rectangle is 9in. We also know the width is a third of the length. Therefore, the width is 3in. So, we can substitute. We get

$P = 2(9\text{in}) + 2(3\text{in})$

$P = 18\text{in} + 6\text{in}$

$P = 24\text{in}$

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Example Question #311 :Geometry And Graphs

The perimeter of a square is 68in. Find the length of one side.

Possible Answers:

$17\text{in}$

$13\text{in}$

$14\text{in}$

$16\text{in}$

$\text{There is not enough information to solve the problem.}$

Correct answer:

$17\text{in}$

Explanation:

正方形有4个等边。找周长of a square, we will use the following formula:

P = 4a

whereais the length of one side of the square. Because a square has 4 equal sides, we can use any side in the formula. To find the length of one side, we will solve fora．

Now, we know the perimeter of the square is 68in. So, we can substitute and solve fora．

$68\text{in} = 4a$

$\frac{68\text{in}}{4} = \frac{4a}{4}$

$17\text{in} = a$

$a = 17\text{in}$

因此,广场的一边的长度17in.

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GED Math : Squares, Rectangles, and Parallelograms

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #301 :Geometry And Graphs

Example Question #302 :Geometry And Graphs

Example Question #303 :Geometry And Graphs

Example Question #304 :Geometry And Graphs

Example Question #305 :Geometry And Graphs

Example Question #306 :Geometry And Graphs

例子问题# 307:Geometry And Graphs

Example Question #308 :Geometry And Graphs

Example Question #309 :Geometry And Graphs

Example Question #311 :Geometry And Graphs

All GED Math Resources

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