Question

3.
If the base of a right angle triangle is 48 cm and its hypotenuse is 50 cm. then find the area
of the triangle
​

Answer 1

Given :

Base of a right angle triangle is 48 cm and its hypotenuse is 50 cm.

To find :

Area  of the triangle.

Solution :

In a right angled triangle, using pythagoras theorem :

Base² + Height² = Hypotenuse²

In the given triangle :

⇒ 48² + Height² = 50²

⇒ Height² = 50² - 48²

⇒ Height² = 196

⇒ Height = √196

⇒ Height = 14 cm.

Now area of triangle :

⇒ Area of right angle Δ = 1/2 × Base × Height

⇒ Area of right angle Δ = 1/2 × 48 × 14

⇒ Area of right angle Δ = 24 × 14

⇒ Area of right angle Δ = 336 cm²

∴ Area of the triangle = 336 cm²

Answer 2

Given

• Base of right angle triangle = 48 cm
• Hypotenuse of right angle triangle = 50 cm

To find

• Area of the right angle triangle

Solution

• In ΔABC
• BC² + AB² = AC² (Pythagoras theorem)
• Base² + Height² = Hypotenuse²
• Height² = Hypotenuse² - Base²
• Height² = 50² - 48²
• Height² = 2500 - 2304
• Height² = 196
• Height = √196
• Height = 14

Hence, the height of right angle triangle is 14 cm

Now, let's find area of ΔABC

• Area of triangle = 1/2 × base × height
• Area of triangle = 1/2 × 48 × 14
• Area of triangle = 24 × 14
• Area of triangle = 336

Hence, the area of triangle is 336 cm²