Question

The perimeters of five squares are $24cm,32cm,40cm,76cm$ and $80cm$ respectively. The perimeter of another square equal in area to the sum of the areas of these squares is:

• A. $31cm$
• B. $62cm$
• C. $124cm$
• D. $961cm$

Answer 1

The correct option is C $124cm$

Total area of five squares
$={\left(\frac{24}{4}\right)}^2+{\left(\frac{32}{4}\right)}^2+{\left(\frac{40}{4}\right)}^2+{\left(\frac{76}{4}\right)}^2+{\left(\frac{80}{4}\right)}^2$
$=6^2+8^2+{10}^2+{19}^2+{20}^2$
$=36+64+100+361+400=961c{m}^2$
$\therefore$ Each side of new square = $\sqrt{961}=31c{m}^2$
$\Rightarrow$ Perimeter = $4\times 31em=124cm.$