Question

1. the length of a rectangle is 1 more than twice the width. the perimeter is 26 feet. what are the dimensions of the rectangle? 2w + 1 w

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2l+2w$, where $l$ is length and $w$ is width. Here $l = 2w + 1$ and $P=26$. Substitute these into the formula: $26=2(2w + 1)+2w$.

Step2: Expand the equation

Expand $2(2w + 1)$ to get $4w+2$. So the equation becomes $26=4w + 2+2w$.

Step3: Combine like - terms

Combine $4w$ and $2w$ on the right - hand side: $26=6w + 2$.

Step4: Isolate the variable term

Subtract 2 from both sides: $26−2=6w$, which simplifies to $24 = 6w$.

Step5: Solve for $w$

Divide both sides by 6: $w=\frac{24}{6}=4$.

Step6: Solve for $l$

Substitute $w = 4$ into the length formula $l=2w + 1$. So $l=2\times4+1=9$.

Answer:

The width of the rectangle is 4 feet and the length is 9 feet.