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If the hypotenuse of an isosceles right triangle has length of 8, then
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29 Apr 2022, 01:00
29 Apr 2022, 01:00
Expert Reply
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Question Stats:
78% (00:49) correct
21% (00:43) wrong based on 38 sessions
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If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is
A. 4
B. 4√2
C. 8
D. 8√2
E. 16
A. 4
B. 4√2
C. 8
D. 8√2
E. 16
Part of the project: GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: If the hypotenuse of an isosceles right triangle has length of 8, then
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29 Apr 2022, 06:41
29 Apr 2022, 06:41
1
Carcass wrote:
If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is
A. 4
B. 4√2
C. 8
D. 8√2
E. 16
A. 4
B. 4√2
C. 8
D. 8√2
E. 16
Let's sketch the given information.
Let x = the length of each of the two equal sides
From here, we can apply the Pythagorean theorem to write: x² + x² = 8²
Simplify: 2x² = 64
Divide both sides of the equation by 2 to get: x² = 32
This means x = √32 [you'll see why I didn't bother simplifying √32 shortly]
So we have the following:
Triangle area = (base)(height)/2 = (√32)(√32)/2 = 32/2 = 16
Answer: E
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Joined: 12 Sep 2018
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Re: If the hypotenuse of an isosceles right triangle has length of 8, then
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26 Apr 2023, 18:49
26 Apr 2023, 18:49
1
Expert Reply
Carcass wrote:
If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is
A. 4
B. 4√2
C. 8
D. 8√2
E. 16
A. 4
B. 4√2
C. 8
D. 8√2
E. 16
Since the hypotenuse is 8, the leg is 8/√2. Thus, the area is:
(8/√2)^2/2 = 32/2 = 16
Answer: E
