In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.

Question

Philoid · Accepted Answer

a = 11, b = 12, c = 13

s = (a + b + c)/2

⇒ s = (11 + 12 + 13)/2 = 36/2 = 18.

Area(Δ) = √s(s-a)(s-b)(s-c)

⇒ Area(Δ) = √18(18-11)(18-12)(18-13)

⇒ Area(Δ) = √18×7×6×5

⇒ Area(Δ) = 6√105 cm² = 61.48 ∼ 61.5 cm²

Area(Δ) = 1/2 × Base × Altitude

⇒ Area(Δ) = 1/2 × 12 × 10.25

⇒ Area(Δ) = 61.5 cm²

Hence the statement is True.