Question

The altitude of a triangle is four-third the length of its corresponding base. If the altitud, solu
is decreased by 5 cm and the base is increased by 5 cm, the area of the triangle would
remain the same. Find the base and the altitude of the triangle.
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Answer 1

Answer:

Let the length of corresponding base be x.

Thus, altitude will be 35x.

Now, it is given that altitude is increased by 4 cm i.e., 35x+4 and base is decreased by 2 cm i.e., x−2.

The area is same for both.

Therefore, 21×x×35x=21×(35x+4)×(x−2)

⇒35x2=35x2−310x+4x−8

⇒8=32x

⇒x=12

Thus, length of base is 12 cm

and length of altitude is 35×12=20 cm.