Question

Clculate the area of the triangle whose sides are 18 cm, 24 cm and 30 cm in lenth. Also, find the length of the altitude corresponding to the smallest side.

Answer 1

Here, a = 18 cm, b = 24 cm , and c = 30 cm

Therefore, S=18+24+302=36

Area = √S(S−a)(S−b)(S−c)

= √36(36−18)(36−24)(36−30)

=√ 36×18×12×6

= √6×6×6×3×3×4×6

= 6×6×3×2 = 216 cm2

Smallest side = 18 cm

Let, h be the height corresponding to the smallest side.

Area of the triangle = (1/2×base×height)sq units

⇒1/2×base×height=216cm2
⇒18×h=216×2

Therefore, h = 24 cm