Question

square and a rectangle have equal areas. If each side of the square is 18 cm and the
width of the rectangle is 12 cm, find the length of the rectangle​ answer is 27​

Answer 1

Given :-

Area of a square = Area of a rectangle

Length of the side of this square = 18 cm

Then :-

The area of this square :-

$= \texttt{side \: × \: side}$

$= \texttt{18 \: × \: 18}$

$=\color{hotpink}\texttt{ 324} \: \: {\texttt{cm}}^{2}$

Thus, the area of this square = 324 cm²

Which means :-

The area of this rectangle = 324 cm²

Measure of the width of this rectangle = 12 cm

Let the length of this rectangle be denoted by x .

An equation to find x (length of this rectangle) :-

$= \texttt{324} \: = \: x\texttt{ \: × \: 12}$

$= x\texttt{ = } \frac{\texttt{324}}{\texttt{12} }$

$= \color{hotpink}x\texttt{ = 27 \: cm}$

Thus, the length of this rectangle = 27 cm

Let us check whether or not we have found out the correct measure of the length of this rectangle :-

$= \texttt{324 \: = \: 27 \: × \: 12}$

$= \texttt{324 = 324}$

$\hookrightarrow \: \texttt{\color{olive}LHS =\color{hotpink} RHS }$

As the measure of the length we have found out is resulting in the desired area , we can conclude that we have found out the correct measure of the length of this rectangle.

Therefore, the length of this rectangle = 27 cm