Question

an isosceles right angle triangle has area of 8 cm square find the length of its hypotenuse​

Answer 1

Both the perpendicular and base are equal in length.

So Area of triangle = 1/2 x b x h

Let b = h = y

1/2 x y x y = 8

y² = 16

y = 4

So Perpendicular = Base = 4 cm

Now by Pythagoras theorem,

4² + 4² = √ 16+ 16 = √32 = 4√2 cm

So required hypotenuse = 4√2 cm

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Answer 2

Solution:-

• In an isosceles triangle two sides are equal.
• Here the the base and the perpendicular of the triangle are equal in length.

• Area of triangle = 8cm^2

=> 8cm^2 = 1/2 × b × h

=> Put b & h as X

=> 16 = x^2

=> X = 4 cm

So, the length of base and perpendicular are 4cm.

H² = B² + P²

( H is hypotenuse,B is base & P is perpendicular)

=> H^2 = 4^4 + 4^2

=> H^2 = 16 + 16

=> H = √32

=> H = 4√2

=> H = 5.65cm

=> H = 5.7cm

Hypotenuse is 5.7 cm

Note:- ( ^ ) is used for power.

ex. 2² = 2^2

i hope it helps you.