Question

The altitude of a triangle is 6 cm greater than its base if the area of the triangle is 108 cm aq find its vase and altitude

Answer 1

ATQ, the altitude of the triangle is 6cm greater than it's base.

let the base of the triangle be x.

therefore it's altitude = x + 6

given the area of the triangle = 108cm²

➡ 1/2 × b × h = 108cm²

➡ 1/2 × x × (x + 6) = 108cm²

➡ x(x + 6) = 108 × 2

➡ x² + 6x = 216

➡ x² + 6x - 216 = 0

➡ x² + (18x - 12x) - 216 = 0

➡ x² + 18x - 12x - 216 = 0

➡ x(x + 18) - 12(x + 18) = 0

➡ (x + 18) (x - 12) = 0

therefore x = -18 or x = 12

since, base can't be in negative. so the base is 12cm.

and it's altitude = x + 6 = 12 + 6 = 18cm