Question

The altitude of a triangle is three – fifth of the length of the corresponding base. If the altitude is decreased by 4cm and the corresponding base is increased by 20cm, the area of the triangle remains the same. Find the base and the altitude of the triangle .​

Answer 1

Given: The altitude of a triangle is three-fifth of the length of the corresponding base.If the altitiude is decreased by 4 cm and base increased by 20 cm,the area of the triangle remains the same.

To find: The base altitude of the triangle

Solution: Let the base and altitude of the triangle be b cm and h cm respectively.

Therefore,h=$\frac{3}{5}$b

Area of a triangle is given by $\frac{1}{2}$×b×h.

According to the problem,

          $\frac{1}{2}$×(b+20)×(h-4)=$\frac{1}{2}$×b×h

i.e.,(bh+20h-4b-80)=bh

i.e.,20h-4b-80=0

i.e.,5h-b-20=0

i.e.,3b-b-20=0

i.e.,2b=20

i.e.,b=10 cm

h=$\frac{3}{5}$×10

 =6 cm

The base of the triangle is 10 cm and the altitude of the triangle is 6 cm.