The longest side of a right angled triangle is 125m
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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
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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.
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