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% ?
Answer & explanation
Correct answer: option 1
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)