the length of a rectangle is 3 more than its width. if the perimeter is 34, what is the length?\na. 10\nb…
the length of a rectangle is 3 more than its width. if the perimeter is 34, what is the length?\na. 10\nb. 15.5\nc. 18.5\nd. 20
Answer
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 of 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: $34 - 6=4w$, so $28 = 4w$. Divide both sides by 4: $w=\frac{28}{4}=7$.
Step5: Find the length
Since $l = w + 3$, substitute $w = 7$ into the equation: $l=7 + 3=10$.
Answer:
A. 10