Question

a rectangle has a perimeter of 15 inches. if the length is two times the sum of 3 and the width, find the dimensions of the rectangle.

Explanation:

Step1: Define variables

Let the width be $w$. Then the length $l = 2(3 + w)$.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 15$, we substitute $l$ and $P$: $15=2(2(3 + w)+w)$.

Step3: Simplify the equation

First, expand the inner - part: $15=2(6 + 2w+w)$. Then combine like terms inside the parentheses: $15=2(6 + 3w)$. Distribute the 2: $15 = 12+6w$.

Step4: Solve for $w$

Subtract 12 from both sides: $15−12=6w$, so $3 = 6w$. Divide both sides by 6: $w=\frac{3}{6}=\frac{1}{2}$ inch.

Step5: Solve for $l$

Substitute $w=\frac{1}{2}$ into the length formula $l = 2(3 + w)$. Then $l = 2(3+\frac{1}{2})=2\times\frac{7}{2}=7$ inches.

Answer:

The width is $\frac{1}{2}$ inch and the length is 7 inches.