Question

The altitude of a triangle is (2/3) of the length of the corresponding base. If the altitude is
decreased by 1 cm and the base is increased by 4 cm, the area of the new triangle remains the
same. Find the base and the altitude of the original triangle.​

Answer 1

Let x be the side of the base.

The altitude os given by 2/3x

Also , we have another triangle such that base is x+4 and

Altitude is 2/3x - 1

Clearly , given triangles have same area as mentioned.

1/2(x)2/3x = 1/2(2/3x-1)(x+4)

2/3x^2 = 2/3x^2+8/3x-x-4

X-8/3x = -4

8/3x - x = 4

5x = 12

X = 12/5 cm

Base of trinagle is 12 / 5 cm

Altitude is given as 8 / 5 cm

Hope it helps!!!