Question

The base of an isosceles triangle is 120 cm and its area is 810 cm square. Find perimeter by herons formula

Answer 1

Let p = semiperimeter

⇒ Perimeter = 2p

Find the equal length of the isosceles triangle:

let the equal side be x

Perimeter = side 1 + side 2 + side 3

2p = 120 + 2x

2x = 2p - 120

x = p - 60

Solve for p:

Area = √p(p - a)(p - b)( p - c)

810 = √p(p - 120)(p - x )(p - x)

810 = √p(p - 120)(p - x )²

810 = √p(p - 120)(p - (p - 60) )²

810 = √p(p - 120)(p - p + 60 )²

810 = √p(p - 120)(60)²

p(p - 120)(60)² = 810²

p(p - 120) = 182.25

p² - 120p - 182.25 = 0

4p² - 480p - 729 = 0

(2p - 243) (2p + 3) = 0

2p = 243 or 2p = -3

p = 243/2 or p = -3/2 (rejected, since perimeter cannot be negative)

p = 121.5 cm

Find the perimeter:

Perimeter = 2p

Perimeter = 2 x 121.5 = 243 cm

Answer: The perimeter is 243 cm