Question

The perimeter of a right angle triangle is 24 centimetre. If its hypotenuse is 10 centimeter, find the area of triangle
1. 24 cm²
2. 36 cm2
3. 40 cm2
4. 48 cm2

Answer 1

Correct Answer - Option 1 : 24 cm²

Given:

The Perimeter of right angle triangle is 24 cm.

Hypotenuse = 10 cm.

Concept Used:

The Perimeter of a triangle is the sum of the lengths of its all sides.

Formula Used:

In the right-angle triangle, by Pythagoras theorem

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

Area of triangle = (1/2) × (Perpendicular) × (Base)

Calculation:

Let the perpendicular and base of a given right angle triangle be P and B respectively.

Perimeter = P + B + 10

⇒ P + B + 10 = 24

⇒ P + B = 14      ----(1)

Also, by Pythagoras theorem

(10)2 = (P)2 + (B)2

⇒ P² + B² = 100      ----(2)

Now, squaring (1), we get, 

 P2 + B2 + 2 PB = 196

⇒ 100 + 2 PB = 196

⇒ 2 PB = 96

⇒ PB = 48

Now, area of Δ = (1/2) × (P) × (B) = PB/2 = 48/2 = 24 cm²

∴ The area of a given right angle triangle is 24 cm².