Question

An isosceles right triangle has area 8 cm. The length of its hypotenuse is​

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

Answer:

4√2

Step-by-step explanation:

As it is an Iscosceles triangle base and it's height will be equal

let their lenghts be

x and y

As per the condition

x=y

1/2xy=8

1/2yy=8

1/2y^2=8

y^2=16

y=√16

y=4

WE GOT THE TWO SIDES

As per the pythagoreas theorem

AB^2=BC^2+ CA^2

AB^2=4^2+4^2

AB^2=16+16

AB^2=32

AB=√32

AB=√16×2

AB=4√2

HYPOTENUSE OF TRIANGLE IS 4√2

Hope this helps you