Question

the height of a triangle is 2 centimetres more than the base. if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square. find the base and the height of the original triangle.

Answer 1

Base = 11 cm

Height = 13 cm

Explanation:

It is given that the height of a triangle is 2 centimetres more than the base.

Let x cm be the base of triangle. So height of the triangle is x+2 cm.

It is given that if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square.

New height = (x+2)+2 = x+4 cm

Area of a triangle is

`A=(1)/(2)* base* height`

`82.5=(1)/(2)* x* (x+4)`

`165=x^2+4x`

`x^2+4x-165=0`

Splitting the middle term, we get

`x^2+15x-11x-165=0`

`x(x+15)-11(x+15)=0`

`(x+15)(x-11)=0`

Using zero product property, we get

`x=-15,11`

Base of a triangle can not be negative, therefore x=11.

Base = 11 cm

Height = 11+2 = 13 cm

Therefore, the base of original triangle is 11 cm and height is 13 cm.