Question

The length of a rectangle is \[4\] inches more than its width, and its perimeter is \[34\] inches. What is the length and width of the rectangle?

Answer 1

Hint: To solve this question, we will use the formula of the perimeter of the rectangle. As we know, the perimeter of a rectangle is equal to \[2\left( {l + w} \right)\], where \[l\] and \[w\] are the length and width of the rectangle respectively. We will assume the width of the rectangle to be \[x\], then according to the question we will get length as \[\left( {x + 4} \right)\]. By applying the values of length and breadth in the perimeter equation and equating it to \[34\] inches, we get the required dimensions of the rectangle.

Complete step-by-step answer:
As we know, the perimeter of a rectangle is equal to \[2\left( {l + w} \right)\], where \[l\] and \[w\] are the length and width of the rectangle respectively.
Let us consider the width of the given rectangle to be \[x\] inches. Now, as given in the question, the length of a rectangle is \[4\] inches more than its width. So, the length will become \[\left( {x + 4} \right)\] inches.

So, putting the values of length and breadth in the perimeter equation, we get
\[ \Rightarrow {\text{Perimeter of the rectangle}} = 2\left( {x + 4 + x} \right)\]
On adding, we get
\[ \Rightarrow {\text{Perimeter of the rectangle}} = 2\left( {2x + 4} \right)\]
On simplifying, we get
\[ \Rightarrow {\text{Perimeter of the rectangle}} = 4x + 8\]
But, given in the question the perimeter of the given rectangle is given as \[34\] inches. Therefore, on equating, we get
\[ \Rightarrow {\text{34}} = 4x + 8\]
Subtracting \[8\] from both the sides, we get
\[ \Rightarrow 26 = 4x\]
On rewriting, we get
\[ \Rightarrow 4x = 26\]
On dividing both the sides by \[4\], we get
\[ \Rightarrow x = \dfrac{{26}}{4}\]
On calculating, we get
\[ \Rightarrow x = 6.5\]
So, width is \[6.5\] inches and length is \[\left( {6.5 + 4} \right)\] i.e., \[10.5\] inches.
Therefore, the length of the rectangle is \[10.5\] inches and width of the rectangle is \[6.5\] inches.

Note: Perimeter is a path or the boundary that surrounds a shape and can also be defined as the length of the outline of a shape. Depending upon the dimension, the perimeter of different figures can be equal in measure. Also note that the perimeter of a circle is called its circumference and its formula is \[{\text{2}}\pi \times \left( {radius} \right)\].