Question

What happens to the area of a square if its perimeter is tripled?

Answer 1

Step 1:

Perimeter of square$=4\times side$

Let the initial perimeter be $xunit$

Side of the square$=\frac{Perimeter}{4}$

Side of the square$=\frac{x}{4}unit$

Area of square$=side\times side=\frac{x}{4}\times \frac{x}{4}=\frac{x^2}{4}unitsquare$

Step 2:

New perimeter when tripled$=3\times initialperimeter$$=3xunits$

Side of square when perimeter tripled$=\frac{3x}{4}units$

Area of square when perimeter tripled$=\frac{3x}{4}\times \frac{3x}{4}=\frac{9x^2}{16}unitsquare$

Step 3:

Impact on area when perimeter tripled$=\frac{Newarea}{Initialarea}=\frac{{\displaystyle \frac{9x^2}{16}}}{{\displaystyle \frac{x^2}{4}}}=\frac{9}{4}times$

Hence, area of square becomes $\frac{9}{4}times$ of initial area when perimeter is tripled.