Question

How could you find the perimeter of an isosceles right triangle if you (8) already know the area?

Answer 1

The area of a triangle is given in terms of the side lengths (b, h) as

... A = (1/2)bh

If b=h, then we can find the side length as ...

... A = (1/2)b²

... b = √(2A) . . . . . multiply by 2 and take the square root

The hypotenuse (x) can be found from the Pythagorean theorem:

... x² = b² + h² = 2b²

... x = b√2

The perimeter is the sum of the side lengths, so is

... P = b + b + x = 2√(2A) + (√(2A))·√2

... P = (2+√2)·√(2A)