The hypotenuse of an isosceles right triangle has a length of h, and

Question

The hypotenuse of an isosceles right triangle has a length of h, and the triangle has an area of a. Which of the following must be true?

A)  a = 4 * h^2

B)  a = 2 * h^2

C)  a = h^2

D)  4a = h^2

E)  2a = h^2

nkin · Answer

Sides will be h/\sqrt{2} . Area a = (1/2) * (h/\sqrt{2}) * (h/\sqrt{2}) = h^2/4 . Hence 4a = h^2 , Option D. Similar post I found: https://gmatclub.com/forum/in-a-right-i ... fl=similar

gmat1393 · Answer

Its a 45-45-90 Triangle. Therefore sides will be in the ratio 1:1:squareroot2
Hence the other 2 sides will be h/squareroot2

Area of Triangle is 1/2*h/squareroot2*h/squareroot2=a
=> 4a=h^2.

Option D

generis · Answer

Area of isosceles right triangle,  a=\frac{s^2}{2} 
 2a=s^2

Hypotenuse:
 h^2=2s^2 
 \frac{h^2}{2}=s^2 
Substitute for  s^2  in area formula:
 2a=\frac{h^2}{2}

4a=h^2

OR

a=\frac{s^2}{2}=\frac{(\frac{h^2}{2})}{2}=\frac{h^2}{4} 
 a=\frac{h^2}{4} 
 4a=h^2

Answer D

You do not need any of those formulas. Use the Pythagorean theorem, and solve for  s^2  (i.e., don't solve for  s  - it gets squared in area of triangle)

In an isosceles right triangle, sides are equal.
 s=s 
 (1)  Area 
Area of triangle,  a=\frac{b*h}{2} 
 a=\frac{s*s}{2}=\frac{s^2}{2}

(2)  Find hypotenuse in terms of  s^2 :
 s^2+s^2=h^2 
 2s^2=h^2 
 s^2=\frac{h^2}{2}

(3)  Substitute and solve
 a=\frac{s^2}{2}=\frac{(\frac{h^2}{2})}{2}=(\frac{h^2}{2}*\frac{1}{2})=\frac{h^2}{4} 
 a=\frac{h^2}{4} 
 4a=h^2

Answer D

Princ · Answer

OA: D

as it is  45^{\circ}-45^{\circ}-90^{\circ}  triangle , its side will be in ratio  1:1:\sqrt{2}

Hypotenuse =  h 
Base = Height = \frac{h}{\sqrt{2}}

Area, a = \frac{1}{2}*\frac{h}{\sqrt{2}}*\frac{h}{\sqrt{2}} 
 4a=h^2

ScottTargetTestPrep · Answer

An isosceles right triangle has angle measures of 45-45-90. Thus, the two legs are of equal length.

Let x = a leg of the triangle. Using the Pythagorean theorem, we can create the equation:

x^2 + x^2 = h^2

2x^2 = h^2

x^2 = h^2/2

x = h/√2

Recall that in an isosceles right triangle, one leg is the base, and the other leg is the height. Thus, the area of the triangle is ½ x^2, and we have:

½ x^2 = a

½(h/√2)^2 = a

½ (h^2/2) = a

h^2/4 = a

h^2 = 4a

Answer: D

Luca1111111111111 · Answer

How do we know that the hypothenuse is not the base?

Archit3110 · Answer

let side be x each and given that hypotenuse is h 
so 2x^2 = h^2
also area ; x^2 = 2 a
so we can say that

h^2 = 4a 
OPTION D

The hypotenuse of an isosceles right triangle has a length of h, and

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The hypotenuse of an isosceles right triangle has a length of h, and

Prep Toolkit

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