Question

area of isoceles right triangle is 32cm² find its perimeter

Answer 1

as this is a right-angled triangle,
area = 1/2 × base × height
let base=height=x (since, this is an isosceles triangle)
32 cm^2 = 1/2 × x × x
x^2 = 64 cm^2
x = 8cm

let y be the 3rd side
32 = 1/4y √4×x^2- y^2
128/y= √4×8^2 - y^2
(128/y)^2 = 256-y^2
16384/y^2 = 256-y^2
16384 = 256y^2-y^4
y^4 - 256y^2 +16384 = 0
(y^2-128) (y^2-128) = 0

so,
y^2 - 128 = 0
y= 8√2 cm

perimeter = 8 +8 +8√2
= 16 + 11.31
= 27.31 cm