Answer
The length of the rectangle is $11$ inches and the width is $6$ inches.
Work Step by Step
We know that the formula for the perimeter of a rectangle is:
$$P = 2l + 2w$$
We know from the problem that the perimeter is $34$ inches and that the length of the rectangle is $5$ inches more than its width. We put all this information together to get the following equation:
$$34 = 2(w + 5) + 2w$$
We distribute what is in parentheses:
$$34 = 2w + 10 + 2w$$
Combine like terms:
$$34 = 4w + 10$$
Subtract $10$ from both sides to get $w$ on one side of the equation:
$$24 = 4w$$
Divide both sides by $4$ to isolate $w$:
$$w = 6$$
If we know that the length $l$ is $5$ more inches than the width $w$, then we can find $l$ with the following equation:
$$l = 6 + 5$$
Add the right-hand side together to get the value for $l$:
$$l = 11$$
