Question

Area of a right-angled triangle is 30 cm². If its smallest side is 5 cm, then its hypotenuse is ______.

पर्याय

• 14 cm

• 13 cm

• 12 cm

• 11 cm

Answer 1

Area of a right-angled triangle is 30 cm². If its smallest side is 5 cm, then its hypotenuse is 13 cm.

Explanation:

Given, area of a right-angled triangle = 30 cm²

And smallest side i.e. base = 5 cm

We know that,

Area of right angled triangle = `1/2` × Base × Height

∴ 30 = `1/2` × 5 × Height

⇒ Height = `(30 xx 2)/5`

⇒ Height = 12 cm

Now, according to Pythagoras theorem,

(Hypotenuse)² = (Perpendicular)² + (Base)²

⇒ (Hypotenuse)² = (12)² + (5)²  ...[∵ Height = Perpendicular]

⇒ (Hypotenuse)² = 144 + 25

⇒ (Hypotenuse)² = 169

⇒ Hypotenuse = `sqrt(169)`

⇒ Hypotenuse = 13 cm