Question

If the area of an isosceles right triangle is 8 cm, what is the perimeter of the triangle? 

A. 8+\(\sqrt2\) cm² 

B. 8+4\(\sqrt2\) cm² 

C. 4+8\(\sqrt2\) cm² 

D. 12\(\sqrt2\) cm²

Answer 1

In right isosceles ∆ABC 

Area of triangle = \(\frac{1}2\)(Base x Altitude)

8 = \(\frac{1}2\)(x x x) = \(\frac{1}2{x}^2\)

x = \(\sqrt{16}\) = 4 cm

(AC)² = (AB)² + (BC)²

y² = x² + x²

y² = 4² + 4²

y² = \(\sqrt{{4}^2+{4}^2}\) = \(\sqrt{32}\) = 4\(\sqrt2\) cm

Perimeter of ∆ABC = AB + BC + CA = 4 + 4 + \(4\sqrt{2}\)= 8 + \(4\sqrt{2}\) cm