Question

Find the length of hypotenuse of an isosceles right angled triangle having an area of 200 cm. Take 2 is equal to 1.414

Answer 1

In an isosceles triangle,any two sides are equal.So,in this question, base=height or (b=h)
Area of ∆=1/2 × b × h
200=1/2 × b square
400= b square
b=√400 = 20
So, b=h=20
Hypotenuse = √400+400
=20√2
=20×1.414
=28.28

Answer 2

What is the perimeter of an isosceles right-angled triangle having an area of 50 cm square?

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Gregory Allen, MS Mathematics, University of Florida (1987)

Answered Jun 27

The two legs have to be the same (since the triangle is isosceles) so call them x. Since the legs form the right angle, if we call one the base then the other is the height of the triangle to that base. Therefore:

Since this is an isosceles right triangle, i.e. a 45–45–90 triangle, the length of the hypotenuse will be . That makes the perimeter