Question

A square and a rectangle have equal areas. If the side of the square is $24cm$and the width of the rectangle is $16cm,$Find the length in $cm$ and the area of the rectangle in $c{m}^2$

Answer 1

Given that ,

Area of rectangle $=$Area of square

Side of the square $=24cm$

The breadth of a rectangle $=16cm$

Let the length of the rectangle $=acm$

Area of rectangle $=$Area of square

$length\times breadth=Side\times SIde$

$$\begin{gathered} a\times 16=24\times 24 \\ a=\frac{24\times 24}{16} \\ a=36 \end{gathered}$$

So, the Length of the rectangle is $36cm$.

Area of Rectangle $=l\times b$

$$\begin{gathered} =36\times 16 \\ =576 \end{gathered}$$

Hence, the Area of Rectangle is $576c{m}^2$.