GRE Math : How to find the perimeter of an acute / obtuse isosceles triangle

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Example Question #1 :Triangles

What is the perimeter of an isosceles triangle given that the sides 5 units long and half of the base measures to 4 units?

Possible Answers:

Correct answer:18

Explanation:

The base of the triangle is 4 + 4 = 8 so the total perimeter is 5 + 5 + 8 = 18.

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Example Question #1 :Triangles

An acute Isosceles triangle has two sides with lengthand one side length. The length of side $\small a=$ $\small \frac{3}{9}$ ft. If the length of $\small b=$ half the length of side $\small a$ , what is the perimeter of the triangle?

Possible Answers:

$\small \frac{2}{6}$ foot

$\small 10$ inches

$\small 6$ inches

$\small 1$ foot

$\small \frac{4}{6}$ foot

Correct answer:

$\small 10$ inches

Explanation:

This Isosceles triangle has two sides with a length of $\small \frac{3}{9}$ foot and one side length that is half of the length of the two equivalent sides.

To find the missing side, double the value of side $\small a$ 's denominator:

$\small \frac{3}{9}=\frac{1}{3}$ . Thus, half of $\small \frac{1}{3}=\frac{1}{6}$ .

Therefore, this triangle has two sides with lengths of $\small \frac{1}{3}$ and one side length of $\small \frac{1}{6}$ .

To find the perimeter, apply the formula:

$\small p=2a+b$

$\small p=\frac{1}{3}+\frac{1}{3}+\frac{1}{6}$

$\small p=\frac{2}{6}+\frac{2}{6}+\frac{1}{6}=\frac{5}{6}=\frac{10}{12}$ foot $\small = 10$ inches

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Example Question #3 :Triangles

An acute Isosceles triangle has two sides with lengthand one side length. The length of side $\small a=$ $\small 13$ . If the length of $\small b=$ half the length of side $\small a$ , what is the perimeter of the triangle?

Possible Answers:

$\small 32.5$

$\small 26.5$

$\small 34.5$

$\small 34$

$\small 26$

Correct answer:

$\small 32.5$

Explanation:

To solve this problem apply the formula: $\small p=2a+b$ .

However, first calculate the length of the missing side by: $\small 13\div2=6.5$ .

Thus, the solution is:

$\small p=13+13+6.5=32.5$

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Example Question #4 :Triangles

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above.

Possible Answers:

$\small \small 60$

$\small 133$

$\small 132$

$\small 120$

$\small 130$

Correct answer:

$\small 132$

Explanation:

To solve this problem apply the formula: $\small p=2a+b$ .

However, first calculate the length of the missing side by:

$\small p=2(a)+12$

$\small a=12\times5=60$

$\small p=2(60)+12$

$\small p=120+12=132$

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Example Question #5 :Triangles

An obtuse Isosceles triangle has two sides with lengthand one side length. The length of side $\frac{3}{4}$ ft. If the length ofhalf the length of side, what is the perimeter of the triangle?

Possible Answers:

$1\frac{2}{3}$ ft

$\frac{12}{4}$ ft

$1\frac{1}{3}$ ft

$1\frac{1}{2}$ ft

Correct answer:

$1\frac{1}{2}$ ft

Explanation:

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that $b=\frac{3}{4}$ ft and that the sides with lengthare half the length of side, find the length ofby: $\frac{3}{4}=\frac{6}{8}$ and half of $\frac{6}{8}=\frac{3}{8}$ . Thus, both of sides with lengthmust equal $\frac{3}{8}$ ft.

Now, apply the formula: p=2a+b .

$p=\frac{3}{8}+\frac{3}{8}+\frac{6}{8}=\frac{12}{8}$

Then, simplify the fraction/convert to mixed number fraction:

$\frac{12}{8}=\frac{3}{2}=1\frac{1}{2}$

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Example Question #6 :Triangles

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above.

Possible Answers:

$\small \frac{35}{3}$

$\small 27$

$\small \frac{56}{3}$

$\small 18$

$\small 21$

Correct answer:

$\small 21$

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

Each of the missing sides equal:

$\small a=\frac{7}{3}\times4=\frac{28}{3}$

Then apply the perimeter formula:
$\small p=\frac{28}{3}+\frac{28}{3}+\frac{7}{3}=\frac{63}{3}=21$

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Example Question #7 :Triangles

Isos._gre_series_

An acute Isosceles triangle has two sides with lengthand one side length. The length of side $\small a=$ inches. If the length of $\small b=$ $\sqrt[3]{a}$ , what is the perimeter of the triangle?

Possible Answers:

inches

Correct answer:

inches

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$b=\sqrt[3]{a}=\sqrt[3]{8}=2$

Then plug each side length into the perimeter formula:

p=2(8)+2=16+2=18

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Example Question #8 :Triangles

Isos._gre_series_

An acute Isosceles triangle has two sides with lengthand one side length. The length of side $\small a=$ $\sqrt{144}$ inches. If the length of $\small b=a\times \frac{1}{2}$ , what is the perimeter of the triangle?

Possible Answers:

$\small 2$ feet

$\small 2.7$ feet

$\small 18$ inches

$\small 30$ inches

$\small 32$ inches

Correct answer:

$\small 30$ inches

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$\small a=\sqrt{144}=12$

$\small b=12\times \frac{1}{2}=\frac{12}{2}=6$

Then, apply the perimeter formula by plugging in the side values:

$\small p=2(12)+6=24+6=30$

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Example Question #9 :Triangles

An acute Isosceles triangle has two sides with lengthand one side length. The length of side $\small a=$ $\small \small \frac{3}{12}$ ft. If the length of $\small b=\small a\times \frac{1}{3}$ , what is the perimeter of the triangle?

Possible Answers:

$\small \frac{3}{4}$ foot

$\small 6$ inches

$\small \frac{1}{4}$ foot

$\small 7$ inches

$\small \frac{9}{12}$ foot

Correct answer:

$\small 7$ inches

Explanation:

To solve this problem apply the formula: $\small p=2a+b$ .

However, first calculate the length of the missing side by:

$\small \frac{3}{12}+\frac{3}{12}+(\frac{3}{12}\times\frac{1}{3})$ , Note that $\small \frac{3}{36}=\frac{1}{12}$

$\small \small \frac{6}{12}+\frac{3}{36}=\frac{6}{12}+\frac{1}{12}=\frac{7}{12}$ .

Since, it takes $\small 12$ inches to make one foot, the perimeter is equal to $\small 7$ inches.

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Example Question #10 :Triangles

An acute Isosceles triangle has two sides with lengthand one side length. The length of side $\small a=$ $\small 8$ inches. The length of side $\small b=$ $\small a\times \frac{1}{4}$ . Find the perimeter of the triangle.

Possible Answers:

$\small 18$ inches

$\small 19$ inches

$\small 14$ inches

$\small 12$ inches

$\small 13$ inches

Correct answer:

$\small 18$ inches

Explanation:

To find the perimeter of this triangle, apply the formula:

$\small p=2a+b$

$\small p=2(8)+(8\times \frac{1}{4})$

$\small p=16+\frac{8}{4}$

$\small p=16+2=18$

Note: Since this is an acute Isosceles triangle, the length of the base must be smaller than the length of both of the equivalent sides.

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GRE Math : How to find the perimeter of an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for GRE Math

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Example Question #1 :Triangles

Example Question #1 :Triangles

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