A isosceles right triangle has area of 12.5 then the length of the hyp

Question

A isosceles right triangle has area of 12.5 then the length of the hypotenuse is

A.  12.5\sqrt{2}

B.  5\sqrt{3}

C.  5\sqrt{2}

D. 5

E.  \sqrt{2}

PKN · Answer

An isosceles right angled triangle is a 45-90-45 triangle, its sides are in the ratio x:\sqrt{x}:1

Given Area=12.5
Or,  \frac{1}{2}*x*x=12.5 
Or,  x^2=25 
Or, x=5

So, hypotenuse=\sqrt{2}x= 5\sqrt{2}

Ans. (c)

Abhishek009 · Answer

\frac{1}{2}a^2 = \frac{25}{2}  ( As  12.5 = \frac{25}{2}  )

So, we can safely conclude that  a = 5

Now, Hypotenuse of the isosceles right triangle =  5\sqrt{2}  , Answer must be (C)

generis · Answer

(1)  Find side length from area
Area of right isosceles triangle*:  \frac{s^2}{2}=12.5 
 s^2=25 
 s=5

(2)  Hypotenuse length? Pythagorean theorem
 s^2 +s^2 = h^2 
 25+25=h^2 
 h^2=50 
 \sqrt{h^2}=\sqrt{(25*2)} 
 h=5\sqrt{2}

Answer C

Faster: an isosceles right triangle is the special 45-45-90 triangle

The sides opposite those angles are in the ratio  x: x: x\sqrt{2} . 
Find  s , which is opposite the 45° angle and hence corresponds with  x  -- then multiply by  \sqrt{2}

From above,  s=5 
Hypotenuse, opposite the 90° angle, corresponds with  x\sqrt{2} 
 x=5 
Hypotenuse =  5\sqrt{2}

Answer C

*The  perpendicular  legs of ANY right triangle are its base and height. In an isosceles right triangle, legs (non-hypotenuse sides) are equal. 
Thus area of a right isosceles triangle is 
 A=\frac{b*h}{2}=\frac{s*s}{2}=\frac{s^2}{2}

ScottTargetTestPrep · Answer

We can let n = the leg of the triangle and create the equation:

n^2/2 = 12.5

n^2 = 25

n = 5

So the hypotenuse is 5√2.

Answer: C

A isosceles right triangle has area of 12.5 then the length of the hyp

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A isosceles right triangle has area of 12.5 then the length of the hyp

Prep Toolkit

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My Rewards