Question

The height of a triangle is increased by 40%. What can be the maximum percentage increase in length of the base so that the increase in area is restricted to maximum of 60%?

Answer 1

Answer:

14.28%

Step-by-step explanation:

Area of Triangle, A = 1/2×b×h

New Area of Triangle, A = 60% increased of A= A + 60% of A = 8A/5

New height = h + 40% of h = 7h/5

Let the new base be x.

8A/5 = 1/2 * x * 7h/5

8/5(1/2*b*h) = 1/2 * 7/5 * x * h

8b = 7x

x = 8b/7

Maximum increase in length of the base = (8b/7 -b) = b/7

Maximum percentage increase in the length of base = (b/7)/b × 100 = 1/7 × 100 = 14.28%

Hope it helps :)