Question

the length of a rectangle is four more than double the width. if the perimeter is 122 inches, find the dimensions. the width is enter your answer inches. the length is enter your answer inches. attempts: 0 submit answer find this question difficult? do you know you can practice another version of this 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 for a rectangle is $P=2(l + w)$. Substitute $l = 2w + 4$ and $P = 122$ into the formula: $122=2((2w + 4)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $122=2(3w + 4)$. Then distribute the 2: $122 = 6w+8$.

Step4: Solve for $w$

Subtract 8 from both sides of the equation: $122−8=6w$, so $114 = 6w$. Divide both sides by 6: $w=\frac{114}{6}=19$ inches.

Step5: Solve for $l$

Substitute $w = 19$ into the length formula $l = 2w+4$. Then $l=2\times19 + 4=38 + 4=42$ inches.

Answer:

The width is 19 inches.
The length is 42 inches.