Question

An isosceles triangle (righ angled) has area 200cm². Find the length of its hypotenuse.

Thank you.

Answer 1

20Rt2 cm
See the attachment

Answer 2

Hey friend, Harish here.

Here is your  answer:

Given that:

1) It is a Isosceles Right angled triangle

2)Area of the triangle is 200cm²

To find,

Hypotenuse of the triangle. 

Let us assume that, The equal  side = x cm & Hypotenuse = y cm.

We Know that ,

Area of a right  angled triangle  = 0.5 × Base × Height
 
                                  200 cm²   = 0.5 × x × x
 
                                  200 cm²   = 0.5 × x²
 
                                            x²   = 400.

                                            x    = 20cm 
                                

Now, We know  that,  

$hypotenuse= \sqrt{ x^{2} + x^{2} }$

                   $= \sqrt{20^{2}+20^{2}}$
 
                   $= \sqrt{400 +400}$
 
                   $= 20 \sqrt{2} cm$

Therefore length  of hypotenuse = 20√2cm
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Hope  my answer is helpful to u.