Question

1. the length of a rectangle is 4 centimeters more than twice its width. if the perimeter of the rectangle is 86 centimeters, find the dimensions of the rectangle.

Explanation:

Step1: Define variables

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

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Substitute $l = 2w + 4$ and $P = 86$ into the formula: $86=2((2w + 4)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $86=2(3w + 4)$. Then distribute the 2: $86 = 6w+8$.

Step4: Solve for $w$

Subtract 8 from both sides: $86 - 8=6w$, so $78 = 6w$. Divide both sides by 6: $w=\frac{78}{6}=13$ centimeters.

Step5: Solve for $l$

Substitute $w = 13$ into the length formula $l = 2w+4$. Then $l=2\times13 + 4=26 + 4=30$ centimeters.

Answer:

The width of the rectangle is 13 centimeters and the length is 30 centimeters.