If the height of a triangle is increased by 30% and its base is decreased by 20%, then what will be the effect on its area?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4% increase
The area of a triangle is \(\frac{1}{2}\times\text{base}\times\text{height}\), so the area changes by the product of the two factors by which the base and the height change.
New height \(=1.30\times\) old height; new base \(=0.80\times\) old base
New area \(=1.30\times0.80=1.04\times\) old area
Change \(=1.04-1=0.04\), that is, a 4% increase
Shortcut: For two successive changes of \(a\%\) and \(b\%\), the net change is \(\displaystyle a+b+\frac{ab}{100}\) per cent.
\(\displaystyle 30+(-20)+\frac{30\times(-20)}{100}=30-20-6=4\), so a 4% increase