ISEE Upper Level Quantitative : How to find the length of the diagonal of a rectangle
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
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Example Questions
Example Question #1 :How To Find The Length Of The Diagonal Of A Rectangle
这是更大的数量?
(a) The length of a diagonal of a square with sidelength 20 inches
(b) The length of a diagonal of a rectangle with length 25 inches and width less than 10 inches
It is impossible to tell which is greater from the information given
(a) is greater
(a) and (b) are equal
(b) is greater
(a) is greater
The lengths of the diagonals of these rectangles can be computed using the Pythagorean Theorem:
(a)
(b)
Example Question #2 :How To Find The Length Of The Diagonal Of A Rectangle
In Rectangle
这是更大的数量?
(a)
(b)
(a) is greater.
(a) and (b) are equal.
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
The diagonals of a rectangle are congruent and bisect each other. Therefore,
Example Question #3 :How To Find The Length Of The Diagonal Of A Rectangle
Rectangle
(a)
(b)
(a) and (b) are equal.
It is impossible to tell from the information given.
(a) is greater.
(b) is greater.
(a) is greater.
Two consecutive sides of a rectangle and a diagonal form a right triangle, so the length of any diagonal can be determined using the Pythagorean Theorem, substituting
The diagonals of a rectangle bisect each other. Therefore, the distance from a vertex to the point of intersection is half this, and
Example Question #4 :How To Find The Length Of The Diagonal Of A Rectangle
A rectangle has perimeter 140 inches and area 1,200 square inches. Which is the greater quantity?
(A) The length of a diagonal of the rectangle.
(B) 4 feet
(B) is greater
(A) and (B) are equal
(A) is greater
It is impossible to determine which is greater from the information given
(A) is greater
Let
Since the product of the length and width is the area, we are looking for two numbers whose sum is 70 and whose product is 1,200; through trial and error, they are found to be 30 and 40. We can assign either to be
The length of a diagonal of the rectangle
A diagonal is 50 inches long; since 4 feet are equivalent to 48 inches, (A) is the greater quantity.
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