If the perimeter of a right-angled isosceles triangle is

Home » Aptitude » Mensuration » Question

If the perimeter of a right-angled isosceles triangle is (4√2 + 4) cm, the length of the hypotenuse is :

1. 4 cm
2. 6 cm
3. 8 cm
4. 10 cm

Correct Option: A

Using Rule 1,

Let ABC be a right-angled isosceles triangle where
AB = BC = x and ∠B = 90°.
∴ AC = √x² + x⊃ = √2x
∴ Perimeter of the triangle ABC = 4√2 + 4
⇒ x + x + √2x = 4√4 + 4
⇒ 2x + 2x = 4√2 + 4
⇒ 2x + 2x = 2.2√2 + 2.2√2
⇒ x = 2√2
∴ Length of the hypotenuse = √2.x = √2 2.√2 = 4 cm.