Question

1. the perimeter of a rectangle is 16 feet. the length is seven less than twice the width. find the dimensions.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ feet. Then the length $l = 2w - 7$ feet.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 16$ feet, we substitute $l$ and $P$ into the formula: $16=2((2w - 7)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $16 = 2(3w - 7)$. Then distribute the 2: $16=6w-14$.

Step4: Solve for $w$

Add 14 to both sides of the equation: $16 + 14=6w-14 + 14$, which gives $30 = 6w$. Divide both sides by 6: $\frac{30}{6}=w$, so $w = 5$ feet.

Step5: Solve for $l$

Substitute $w = 5$ into the equation for $l$: $l=2(5)-7=10 - 7=3$ feet.

Answer:

The width is 5 feet and the length is 3 feet.