Question

If the altitude of a triangle is increased by 10% while its area remains the same, its corresponding base will have to be decreased by 

(a) 10% 

(b) 9%

(c) \(9\frac{1}{11}\)%

(d) \(11\frac{1}{9}\)%

Answer 1

(c) 9\(\frac{1}{11}\)%

Let the altitude of the triangle be h and corresponding base = b. Then, its area =\(\frac{1}{2}\)bh, Increased altitude = 1.1h,

Area remaining same =\(\frac{1}{2}\)bh

\(\therefore\) Reduced base = \(\frac{\frac{1}{2}bh}{1.1h}\) x 2  = \(\frac{b}{2.2}\) x 2 = \(\frac{10b}{11}\)

\(\therefore\) % reduction = \(\frac{b-\frac{10}{11}b}{b}\)x 100 = \(\frac{100}{11}\)%

= \(9\frac{1}{11}\)%