Question
A square and a rectangle have the same perimeter. Calculate the area of the rectangle is the side of the square is 60 cm and the length of the rectangle is 80 cm .
✓
Answer
Perimeter of square formula = 4 $\times$ Side of the square
Hence, P Square = 4 $\times$ 6 = 240 cm.
Perimeter of rectangle formula = 2 $\times$ (length + breadth)
Hence, P (rectangle) = 2 (80 + Breadth)
= 160 + 2 $\times$ Breadth
According to the question,
$
\begin{array}{rlrl}
160+2 \times \text { Breadth } =240 cm . \\
\Rightarrow 2 \times \text { Breadth } =240-160
\end{array}
$
$
\begin{array}{rlrl}
\Rightarrow \text { Breadth } =\frac{80}{2}
\end{array}
$
$\therefore$ The breadth of the rectangle = 40 cm Now, the area of rectangle $=$ length $\times$ Breadth
$
\begin{array}{l}
=80 \times 40 \\
=3200 cm^2
\end{array}
$
Hence, P Square = 4 $\times$ 6 = 240 cm.
Perimeter of rectangle formula = 2 $\times$ (length + breadth)
Hence, P (rectangle) = 2 (80 + Breadth)
= 160 + 2 $\times$ Breadth
According to the question,
$
\begin{array}{rlrl}
160+2 \times \text { Breadth } =240 cm . \\
\Rightarrow 2 \times \text { Breadth } =240-160
\end{array}
$
$
\begin{array}{rlrl}
\Rightarrow \text { Breadth } =\frac{80}{2}
\end{array}
$
$\therefore$ The breadth of the rectangle = 40 cm Now, the area of rectangle $=$ length $\times$ Breadth
$
\begin{array}{l}
=80 \times 40 \\
=3200 cm^2
\end{array}
$
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