The base of a triangle is 18m more than the double of its height. If the area of the triangle be 360 sq-m, then find the height of the triangle.

Explanation

Let the height of the triangle =x m,
`:.` its base =(2x+18)m
`:.` area of the tirangle `=(1)/(2)xx(2x+18)xx""x` sq-m
`=(x^(2)+9x)` sq-m.
As per question, `x^(2)+9x=360`
or, `x^(2)+(24-15)x-360=0`
or, `x^(2)+24x-15x-360=0`
or, `x(x+24)-15(x+24)=0`
or, `(x+24)(x-15)=0`
`:.` either `x+24=0" "or,x-15=0`.
`impliesx=-24" "impliesx=15`
But height can not be negative, `:.xne-24`.
`:.x=15`
Hence the height of the triangle is 15 m.