Question

The base of triangle 18 mtr more than two times of its heights, if the area of the triangle is 360 sq.m. find its height.

Answer 1

Answer:

The height of the triangle is 15m

Step-by-step Explanations :

Given : Base = 18 m more than two times of its height

Area = 360 m²

To find : height of Triangle = ?

let, the height of the triangle be x metre,

Then according to given condition,

Base of the talangle = (2x+18) m

Area of the triangle = 360 m² ..( given )

We know that,

Area of Triangle = 1/2 × base × height

Substituting the given value in above formula we get,

1/2 × ( 2x + 18 ) × x = 360

x/2 × ( 2x + 18 ) = 360

x × ( x + 9 ) = 360

x² + 9x = 360

x² + 9x - 360 = 0

x² + 24x - 15x - 360 = 0

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

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

Either x + 24 = 0 ∴ x = -24

Also, x - 15 = 0. ∴ x = 15

Since height cannot be -ve.

x = 15 m

Hence, the height of the triangle is 15m