Question

The perimeter of a rectangle is 96 feet. How do you find the dimensions of the rectangle if the ratio of the length to the width is $7:5$ ?

Answer 1

Hint: In this question, we need to find the dimensions of the rectangle for the given perimeter and length width ratio. To find the dimensions length and width, we use the formula to find the perimeter of the rectangle which is given by $2(l + w)$. Then substitute the values and simplify the expression. Then we obtain the required values of dimensions of the rectangle.

Complete step by step answer:
Given the perimeter of the rectangle 96 feet.
Also given that the ratio of length to the width as $7:5$
We are asked to find the dimensions of the rectangle.
i.e. we need to find the values of length and width of a rectangle given.
The perimeter is usually defined as the boundary or the path that surrounds a two-dimensional shape.
The perimeter P of the rectangle is calculated using the formula,
$P = 2(l + w)$ …… (1)
where $l$ is the length and $w$ is the width of the rectangle.
The ratio of dimensions ( length : width) is given as $7:5$.
Let us denote the dimensions as,
Length $(l) = 7x$ and Width $(w) = 5x$ …… (2)
We have the perimeter value as $P = 96$ feet.
Substituting these values in the equation (1), we get,
$ \Rightarrow 96 = 2(7x + 5x)$
Adding the terms inside the parenthesis and simplifying we get,
$ \Rightarrow 96 = 2(12x)$
$ \Rightarrow 96 = 24x$
Dividing the both sides of the equation by 24, we get,
$ \Rightarrow \dfrac{{96}}{{24}} = \dfrac{{24x}}{{24}}$
Cancelling the common terms and simplifying we get,
$ \Rightarrow x = 4$
So now we determine the dimensions of the rectangle by using the value of x
Substituting $x = 4$ in the equation (2), we get,
Length $(l) = 7x$
$ \Rightarrow 7 \times 4 = 28$ feet
Width $(w) = 5x$
$ \Rightarrow 5 \times 4 = 20$ feet

Hence the dimensions of the rectangle are given by length is 28 feet and width is 20 feet.

Note: We can verify whether obtained values of the dimensions which are length and width are correct by substituting back it in the formula of finding the perimeter of a rectangle. If the L.H.S. is equal to R.H.S. then our solution is correct.
The perimeter is usually defined as the boundary or the path that surrounds a two-dimensional shape
Students must know the formula to find the perimeter of a rectangle which is given by,
$P = 2(l + w)$
where $l$ is the length and $w$ is the width of the rectangle.