A rectangle's length is 10 inches greater than its width. If the perimeter of the rectangle is 68 inches, find the length. (All answers are given in inches.)

Question

High School

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Answer :

AbheeBridge AbheeBridge · Answer 1 · 2024-04-05T13:43:28-04:00

The length of the rectangle is 22 inches.

To find the length of the rectangle, we need to use the information given in the problem. Let's start by defining the variables:

Let [tex]w[/tex] represent the width of the rectangle.
Since the length is 10 inches greater than the width, we can express the length as [tex]w + 10[/tex].
The formula for the perimeter [tex]P[/tex] of a rectangle is given by:
[tex]P = 2(l + w)[/tex]

We are told the perimeter of the rectangle is 68 inches, so we can write:

[tex]68 = 2((w + 10) + w)[/tex]

Simplify inside the parentheses:

[tex]68 = 2(2w + 10)[/tex]

Distribute the 2:

[tex]68 = 4w + 20[/tex]

Subtract 20 from both sides of the equation:

[tex]48 = 4w[/tex]

Divide both sides by 4 to solve for [tex]w[/tex]:

[tex]w = 12[/tex]

Now that we know the width [tex]w[/tex] is 12 inches, we can find the length by adding 10 to the width:

[tex]l = w + 10 = 12 + 10 = 22[/tex]