Question

The length of a rectangle is 4 more than twice its width. The perimeter is 28 units. Write an expression to find the length of the rectangle.

Answer 1

Hint: In the given question we are given a rectangle. In the given rectangle we are also provided the relation between the length and breadth of it. Now we are being asked to find the length of the rectangle when the perimeter of the same rectangle is provided to us.

Complete step by step solution:
As per the given question, we need to find the length of the rectangle when we know that the perimeter is given and also, we know the relation between the length and breadth of the rectangle.
Now, we know that the perimeter of the rectangle is 28 units.
Length of the rectangle is four more than twice its breadth.
Let the breadth of the rectangle be b and length be l, then $l=2b+4$ .
Also, we know that the perimeter of the rectangle is given by $2\left( l+b \right)$ and this is equal to 28 units.
Therefore,
$\begin{align}
  & 2\left( 2b+4+b \right)=28 \\
 & \Rightarrow 6b+8=28 \\
 & \Rightarrow 6b=20 \\
 & \Rightarrow b=\dfrac{20}{6} \\
 & \Rightarrow b=\dfrac{10}{3} \\
\end{align}$
And length of the rectangle would be
$\begin{align}
  & l=2\times \dfrac{10}{3}+4 \\
 &\Rightarrow l=\dfrac{20+12}{3} \\
 &\Rightarrow l=\dfrac{32}{3} \\
\end{align}$
Therefore, the length of the rectangle is $\dfrac{32}{3}$ .

Note: In such questions we need to be very careful with the calculations as this is very common. Apart from this we need to be aware of the properties of the rectangle and the way of finding the perimeter. Also, we must know how the perimeter of the rectangle is found and then proceed to find the answer.