The figure shows nine identical rectangles fitted together to make a large rectangle whose area is 72 cm² Class 9

The figure shows nine identical rectangles fitted together to make a large rectangle whose area is 72 cm² Class 9

Question 1.

The figure shows nine identical rectangles fitted together to make a large rectangle whose area is 72 cm² Find the perimeter of each small rectangle. Class 9

Solution:

Given:

Area of large rectangle = 72 cm²

9 identical rectangles together forms the large rectangle

∴ Area of one rectangle = $\frac{72}{9}$ = 8 cm² ... (i)

Let the length of each small rectangles be l cm and breadth be w cm.

∵ From the figure, total width of larger rectangle remains same.

∴ 4l = 5w

∴ l = $\frac{5}{4}$w ...(ii)

But Area of one rectangle = 8 cm² ...[From (i)]

∵ lw = 8

$\left(\frac{5}{4} w\right) \times w=8 \quad \ldots[$ From (ii) $]$

$\begin{array}{ll} & \frac{5}{4} w^2=8 \\ \therefore & w^2=\frac{32}{5} \\ \therefore & w=\sqrt{\frac{32}{5}}=\frac{4 \sqrt{10}}{5} \mathrm{~cm} .\end{array}$

$l=\frac{5}{4} \times \frac{4 \sqrt{10}}{5} \quad \ldots[$ From (ii) $]$

∴ l = $\sqrt{10}$

∵ Perimeter of each small rectangle

= 2(Length + Breadth)

= 2(l + w)

$\begin{aligned} & =2\left(\sqrt{10}+\frac{4 \sqrt{10}}{5}\right) \\ & =2\left(\frac{5 \sqrt{10}+4 \sqrt{10}}{5}\right) \\ & =2\left(\frac{9 \sqrt{10}}{5}\right) \\ & =\frac{18 \sqrt{10}}{5}\end{aligned}$

∴ Perimeter of each small rectangle

$=\frac{18 \sqrt{10}}{5} \mathrm{~cm}$