An altitutde of a triangle is five –thirds the length of its corresponding base. If the altitude were increased by 4 cm and the base be decreased by 2 cm, the area of the triangle would remain the same. Find the base and the altitude of the triangle.

Explanation

Let the base of the triangle be `x`cm.
Then the altitude of the triangle will be `5/3x`cm.
The original area of the triangle`=1/2timesxtimes5/3`
Now,
Given that:
Altitude is increased by `4` cm`=5/3x+4`
And base is decreased by `2`cm`=x−2`.Then,
Area of a new triangle`=1/2times(x-2)times(5/3x+4)`
According to the question:
`1/2timesxtimes5/3x=1/2times(5/3x+4)times(x−2)`
`5/3x^2=5/3x^2-10/3x^2+4x-8`
`8=2/3x`
`x=12`
`therefore`The base of the triangle`=12`cm.
The altitude of the triangle`=5/3times12=20`cm.