Question

A field is in the form of a right triangle with hypotenuse 50 m and one side 30 m. Find the

area of the field.

​

Answer 1

Area of right angled triangle

= 1/2 × base ×height

= 1/2 × 30 × 50 = 750m²

Answer 2

// FIND THE HEIGHT //

• Base = 30m
• hypotenuse = 50m
• let height = x

$\large\boxed{ According \: \: to \: \: \: Pythagorean \: \: theorem }$

⟹ (Base)² + (height)² = (hyp.)²

⟹ (30m)² + (x)² = (50m)²

⟹ 900m² + x² = 2500m²

⟹ x² = 2500m² - 900m²

⟹ x² = 1600m²

⟹ x = √1600m²

⟹ x = 40m

So, height of the field = 40m

______________________________________

// FIND THE AREA //

• formula for area of right angle triangle:

$\large\boxed{Area = 1/2 × height × base}</p><p></p><p>$

Area = 1/2 × 40m × 30m

= 1/2 × 1200m²

= 600m²

600m² is the answer.