Question

An equilateral triangle has length of each edge as $25$cm. If the side of the triangle is increased by $30\%$, then find the percentage increase in its perimeter.

Answer 1

Length of equilateral triangle$=$$25$cm

STEP 1:- First find the new length

increase of side$=$$30\%$of original side

$=$$\frac{30}{100}\times 25$

$=7.5$cm

New Length of the equilateral triangle$=25+7.5$

$=32.5\mathrm{cm}$

STEP 2:- Find the perimeter

Formula to calculate the perimeter

The perimeter of an equilateral triangle$=$$3\times \mathrm{side}$

Old perimeter$=$$3\times \mathrm{side}$

$=$$3\times 25$

$=75\mathrm{cm}$

New perimeter$=$$3\times \mathrm{side}$

$=3\times 32.5$

$=97.5\mathrm{cm}$

STEP 3:- Now calculate the percentage increase in its perimeter.

Difference in perimeter$=$New perimeter $-$ old perimeter

$$\begin{gathered} =97.5-75 \\ =22.5 \end{gathered}$$

percentage increase in its perimeter$=$$\left(\frac{\mathrm{Difference}}{\mathrm{Orignal}\mathrm{value}}\times 100\right)\%$

$$\begin{gathered} =\left(\frac{22.5}{75}\times 100\right)\% \\ =\left(0.3\times 100\right)\% \\ =30\% \end{gathered}$$

Hence, the perimeter will increase by $30\%$.