Question

the base of a triangle exceeds twice its altitude by 18m if the area of the triangle be 360 sq.m what is it's altitude?​

Answer 1

Answer:

Area of a triangle is 1/2 base x height. Let's call the height h. Base is 2h + 18 (twice its height + 18). You know 1/2 base x height = 360. Plug in h for height and 2h+18 for base.

1/2(2h+18) x h = 360

Multiply the parenthesis by 1/2. (h + 9) x h = 360

Then solve for h.

Answer 2

Given - Base of triangle exceeds twice its altitude by 18 metre

Area of triangle = 360 square metre

Find - Altitude of triangle

Solution - Area of triangle is calculated by the formula = 1/2 * base * height

Let us assume height of triangle be x.

Base of triangle = 2x + 18

Keeping the values in formula-

Area = 1/2 * (2 x + 18) * x

360 = 1/2 *(2 x + 18) * x

360 = 1/2 * 2 (x + 9) * x

360 = (x + 9) * x

x² + 9x - 360 = 0

x² - 15x + 24x - 360 = 0

x (x - 15) + 24 (x - 15) = 0

(x - 15) (x + 24) = 0

Hence, x = -24, 15.

Therefore, altitude of triangle is 15 metre.