Question

A triangle has an area of 90 cm²? Find the length of the base if the base is
3 cm more than height.

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Answer 1

Answer:

Given : Area = 90 cm².

let height be x and base be (x+3).

Therefore, Area (A) = 1/2 × (x+3) × x.

90 cm² = 1/2 × (x+3) × (x).

180 = (x+3)x.

180 = x² + 3x.

x² + 3x - 180 = 0.

x²- 15x + 12x - 180 = 0.

x(x-15) + 12(x -15) = 0.

(x-15) (x+12) = 0.

x = 15.

Now, the required height is 15cm and the length of the required base is (15+3) i.e, 18cm.