Question

the longest side of a right angled triangle is 125m and one of tge remaining two sides is 100m. Find its area using herons formula

Answer 1

Solution :-

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

Answer.

Answer 2

Given that the longest side of the right angled triangle = 125 m
Since the triangle is right angled triangle, therefore, longest side will be the hypotenuse.
Hence, Hypotenuse = 125 m
One of the remaining two sides = 100 m
Now by the Pythagoras theorem,
(125)² = (100)² + x²
where 'x' is the other side which is unknown.
15625 - 10000 = x²
x² = 5625 
x = 75 m
Perimeter = 75 + 100 + 125
Perimeter = 300 m
Semi-perimeter = 300/2 = 150 m
Area of triangle = A = √[150(150-125)(150-100)(150-75)]
A = √[150(25)(50)(75)]
A = √14062500
A = 3750 m²
Which is the required area of the triangle.