The base of a triangle is increased by 40%. By what percentage (correct to two decimal places) should its height be increased so that the area increases by 60% ?

14.29%

40% = \(\frac{2}{5}\)

60% = \(\frac{3}{5}\)

Ratio of ,              Old    :   New

Base                     5      :     7

Height                   a      :     b

-----------------------------------------------

Area                    5       :     8

-----------------------------------------------

We know ,

Area of triangle = \(\frac{1}{2}\) × Base × Height

According to question ,

\(\frac{5a}{7b}\) = \(\frac{5}{8}\) 

\(\frac{a}{b}\) = \(\frac{7}{8}\) 

The percentage  height increases = \(\frac{(8-7)}{7}\)  × 100

= \(\frac{1}{7}\) × 100

= 14.285...%

= 14.29% (correct to two decimal places)