Question

An isosceles right triangle has area 8 cm². The length of its hypotenuse is ______.

Options

• `sqrt(32)` cm

• `sqrt(16)` cm

• `sqrt(48)` cm

• `sqrt(24)` cm

Answer 1

An isosceles right triangle has area 8 cm². The length of its hypotenuse is `underlinebb(sqrt(32)  cm)`.

Explanation:

Let height of triangle = h

As the triangle is isosceles,

Let base = height = h

According to the question,

Area of triangle = 8 cm² 

⇒ `1/2` × Base × Height = 8

⇒ `1/2` × h × h = 8

⇒ h² = 16

⇒ h = 4 cm

Base = Height = 4 cm

Since the triangle is right angled,

Hypotenuse² = Base² + Height²

⇒ Hypotenuse² = 4² + 4²

⇒ Hypotenuse² = 32

⇒ Hypotenuse = `sqrt(32)`

Hence, the length of its hypotenuse is `sqrt(32)`