Question

The perimeter of a triangular field is 240 m. If two of its sides are 78 m and 50 m, then what is the length of the perpendicular on the side of length 50 m from the opposite vertex? 

(a) 43 m 

(b) 52.2 m 

(c) 67.2 m 

(d) 70 m

Answer 1

(c) 67.5 m

Given 2s = a + b + c ⇒ 240 = 78 + 50 + Third side 

⇒ Third side = 240 m – 128 m = 112 m.

∴ Area of Δ = \(\sqrt{s(s-a)(s-b)(s-c)}\)

= \(\sqrt{120(120-78)(120-50)(120-112)}\)

= \(\sqrt{120\times42\times70\times8}\) = 1680

Also, Area of Δ = \(\frac{1}{2}\)x b x h

 ∴ \(\frac{1}{2}\) x 50 x h = 1680 ⇒ h = \(\frac{1680}{25}\) = 67.5 m.