Question

1. the length of a rectangle is 3 inches more than its width. if the perimeter is 42 inches, find the dimensions of the rectangle.

Explanation:

Step1: Define variables

Let the width of the rectangle be $x$ inches. Then the length is $x + 3$ inches.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2l + 2w$. Substituting $l=x + 3$, $w = x$ and $P = 42$ into the formula, we get $2(x + 3)+2x=42$.

Step3: Expand the equation

Expand $2(x + 3)$ to get $2x+6+2x = 42$.

Step4: Combine like - terms

Combine the $x$ terms: $4x+6 = 42$.

Step5: Solve for $x$

Subtract 6 from both sides: $4x=42 - 6=36$. Then divide both sides by 4, so $x = 9$.

Step6: Find the length

The length $l=x + 3$. Substitute $x = 9$ into it, we get $l=9 + 3=12$.

Answer:

The width is 9 inches and the length is 12 inches.