Question

each side of an equilateral triangle is increased by 1.5%.find the percentage increased in its area

Answer 1

$$\begin{gathered} Letthesideofequilateraltrianglebea \\ so,areaofequilateraltriangle=\frac{\sqrt{3}}{4}{a}^2 \\ Ifsideisincreasedby1.5\% \\ Newside=a+1.5\%ofa=a+\frac{1.5}{100}a=a+.015a=1.015a \\ Newareaofequilateraltraingle=\frac{\sqrt{3}}{4}(1.015a{)}^2=\frac{\sqrt{3}}{4}(1.015a{)}^2=\frac{\sqrt{3}}{4}1.030225a^2 \\ ChangeinArea=\frac{\sqrt{3}}{4}1.030225a^2-\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}0.030225a^2 \\ Percentagechangeinarea=\frac{Changeinarea}{oldarea}\times 100 \\ \%changeinarea=\frac{\frac{\sqrt{3}}{4}0.030225a^2}{\frac{\sqrt{3}}{4}{a}^2}\times 100=0.030225\times 100=3.0225\% \end{gathered}$$