Question

the length of a rectangle is four more than double the width. if the perimeter is 104 inches, find the dimensions. the width is inches. the length is inches. question help: message instructor > next question

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ inches. Then the length $l = 2w + 4$ inches.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 2w + 4$ and $P = 104$ into the formula: $104=2((2w + 4)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $104=2(3w + 4)$. Then distribute the 2: $104 = 6w+8$.

Step4: Solve for w

Subtract 8 from both sides: $104 - 8=6w$, so $96 = 6w$. Divide both sides by 6: $w=\frac{96}{6}=16$ inches.

Step5: Solve for l

Substitute $w = 16$ into the length formula $l = 2w+4$. Then $l=2\times16 + 4=32 + 4=36$ inches.

Answer:

The width is 16 inches.
The length is 36 inches.