Question

The longest side of a right angled triangle is 125m and one of the remaining two sided is 100m. Find its area using Heron's Formula

Answer 1

KryX

Longest side of the triangle or hypotenuse = 125 m

One of the two remaining sides = 100 m

Assume that 100 m is length of the perpendicular

Using Pythagoras Theorem -

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

⇒ (125)² (Base)² + (100)

⇒ 15625 = (Base)² + 10000

⇒ (Base)² = 15625 - 10000

⇒ (Base)² = 5625

⇒ Base = √5625

⇒ Base of third side of triangle = 75 m

Heron's formula of area of triangle = √s(s - a)(s- b)(s - c)

semi perimeter = (a + b + c)/2

⇒ s = (125 + 100 + 75)/2

⇒ s = 300/2

⇒ s = 150 m

Area = √150*(150 - 125)*(150 - 100)*(150 - 75)

⇒ √150*25*50*75

⇒ √14062500

= 3750 m²

So, area of the given triangle is 3750 m²

It'll help!

Answer 2

by herons formula we cannot do this as the third side is not given . If the area of the triangle is asked then it will be 6250m^2