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A right triangle ABC has hypotenuse 20 and base 16.
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04 Aug 2022, 02:53
04 Aug 2022, 02:53
Expert Reply
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Question Stats:
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0% (00:00) wrong based on 9 sessions
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A right triangle ABC has hypotenuse 20 and base 16.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
The area of triangle ABC |
Two times the perimeter of triangle ABC |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: A right triangle ABC has hypotenuse 20 and base 16.
[#permalink]
22 Aug 2022, 10:59
22 Aug 2022, 10:59
Expert Reply
OE
Quote:
Explanation: Fun fact: the areas and perimeters of triangles with legs 12
and 5 or 6 and 8 (talking whole numbers here) are equal. This triangle
has a related relationship; its legs are twice as long as 6 and 8, and its
area is equal to twice its perimeter. But you don’t need to know all that
for this problem. Just use the Pythagorean Theorem to find the height of
the triangle: 162 + h2 = 202, so h2 = 144, so h = 12. (Note that knowing
higher squares off the top of your head is useful.) So the area of the
triangle = ½ bh = ½ (16)(12) = 96, and twice the perimeter is 2(20 + 16
+ 12) = 96.
and 5 or 6 and 8 (talking whole numbers here) are equal. This triangle
has a related relationship; its legs are twice as long as 6 and 8, and its
area is equal to twice its perimeter. But you don’t need to know all that
for this problem. Just use the Pythagorean Theorem to find the height of
the triangle: 162 + h2 = 202, so h2 = 144, so h = 12. (Note that knowing
higher squares off the top of your head is useful.) So the area of the
triangle = ½ bh = ½ (16)(12) = 96, and twice the perimeter is 2(20 + 16
+ 12) = 96.
gmatclubot
Re: A right triangle ABC has hypotenuse 20 and base 16. [#permalink]
22 Aug 2022, 10:59
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