Find the area of a triangle whose sides are respectively 150 cm, 120 c

1.	Find the area of a triangle whose sides are respectively 150 cm, 120 cm, and 200 cm.
Answer» Let a, b and c are the sides of triangle and s is the semi-perimeter, then its area is given by A. \(\sqrt{s(s-a)(s-b)(s-c)}\) where s = \(\frac{a+b+c}{2}\)[Heron’s Formula] a = 150, b = 120, c = 200 s = \(\frac{a+b+c}{2}\) = \(\)\(\frac{100+120+200}{2}\) = 235 A = \(\sqrt{235(235-150)(235-120)(235-200)}\) A = \(\sqrt{235 \times85 \times115 \times35}\) = \(25\sqrt{47 \times17 \times23 \times7}\) = \(25\sqrt{128369}\) cm²

Find the area of a triangle whose sides are respectively 150 cm, 120 cm, and 200 cm.

Answer»

Let a, b and c are the sides of triangle and s is the semi-perimeter, then its area is given by

A. \(\sqrt{s(s-a)(s-b)(s-c)}\) where s = \(\frac{a+b+c}{2}\)[Heron’s Formula]

a = 150, b = 120, c = 200

s = \(\frac{a+b+c}{2}\) = \(\)\(\frac{100+120+200}{2}\) = 235

A = \(\sqrt{235(235-150)(235-120)(235-200)}\)

A = \(\sqrt{235 \times85 \times115 \times35}\) = \(25\sqrt{47 \times17 \times23 \times7}\) = \(25\sqrt{128369}\) cm²