Question

The perimeter of a rectangle is 182 ft. The width is two more feet than the length . Find the length and width.

Answer 1

Let's call the width $w$ and the length $l$ based on this, we can make two equations based on the first and second sentences in the problem.

$w = l + 2$

$2l + 2w = 182$

If we substitute $l + 2$ for $w$ into the second equation, we can make the following:

$2l + 2(l + 2) = 182$

• Substitute

$2l + 2l + 4 = 182$

• Use the Distributive Property

$4l + 4 = 182$

• Combine like terms

$4l = 178$

• Subtract 4 from both sides

$l = \dfrac{178}{4} = \dfrac{89}{2}$

• Divide both sides by 4 and simplify

Now, let's find $w$:

$w = l + 2 = \dfrac{89}{2} + 2 = \dfrac{93}{2}$

The length of the rectangle is $\boxed{\dfrac{89}{2} \,\textrm{ft}}$ and the width of the rectangle is $\boxed{\dfrac{93}{2} \,\textrm{ft}}$.