Question

an altitude of a triangle is 5 by 3 times the length of its corresponding base if the altitude is increased by 4 cm and the base is decreased by to the area of the triangle remains the same find the altitude and the base of the original triangle​

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.