Question

the length of a rectangle is 3 more than its width. if the perimeter is 34, what is the length?
a. 10
b. 15.5
c. 18.5
d. 20

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = w + 3$.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Substitute $l = w + 3$ and $P = 34$ into the formula: $34=2((w + 3)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $34=2(2w + 3)$. Then distribute the 2: $34 = 4w+6$.

Step4: Solve for $w$

Subtract 6 from both sides of the equation: $34 - 6=4w$, so $28 = 4w$. Divide both sides by 4: $w=\frac{28}{4}=7$.

Step5: Find the length

Since $l = w + 3$ and $w = 7$, then $l=7 + 3=10$.

Answer:

A. 10