Question

The area of a rectangle is given by the product of its length and breadth. The length of a rectangle is two third of its breadth. Find its area, if its breadth is x cm.

Answer 1

Hint: According to question, write length and breadth in terms of x and by using area of rectangle (A=l.b) find area in terms of x.

Complete step-by-step answer:
The length of the rectangle =l.
 The breadth of the rectangle = b.
According to question, let the breadth be x then let the length be $\dfrac{2}{3}$ x

∴ Area of Rectangle = lxb
So,
$\begin{array}{l}
 = \dfrac{2}{3}x \times x\\
 = \dfrac{2}{3}{x^2}
\end{array}$
Hence, the area of rectangle = $\dfrac{2}{3}{x^2}$

Note: The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship: A = L ⋅ W. If we know the width, it's easy to find the length by rearranging this equation to get L = A ÷ W. If you know the length and want the width, rearrange to get W = A ÷ L.We can also find perimeter in terms of x by using the formula P=2(l+b)