Question

unit 1 post test year long (total 61 pts)

1. (4 pts) the length of a rectangle is 5 less than twice the width. if the perimeter of the rectangle is 146, find the length and width of the rectangle.

length = ________
width = ________

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = 2w - 5$.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Substitute $l = 2w - 5$ and $P = 146$ into it: $146=2((2w - 5)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $146 = 2(3w - 5)$. Then distribute the 2: $146=6w-10$.

Step4: Solve for $w$

Add 10 to both sides of the equation: $146 + 10=6w$, so $156 = 6w$. Divide both sides by 6: $w=\frac{156}{6}=26$.

Step5: Solve for $l$

Substitute $w = 26$ into the length formula $l = 2w - 5$. Then $l=2\times26 - 5=52 - 5 = 47$.

Answer:

Length = 47
Width = 26