Question

1. rectangle dimensions (word problem notes)

the perimeter of a rectangle is 238 feet. the length is (5x + 10) and the width is (3x + 5). what are the actual dimensions of the rectangle?
a) length = 44 ft, width = 75 ft
b) length = 70 ft, width = 40 ft
c) length = 75 ft, width = 44 ft
d) length = 85 ft, width = 50 ft

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$. Given $P=238$, $l=(5x + 10)$ and $w=(3x + 5)$. So, $238=2((5x + 10)+(3x + 5))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(5x + 10)+(3x + 5)=8x + 15$. Then the equation becomes $238 = 2(8x + 15)$. Divide both sides by 2: $119=8x + 15$.

Step3: Solve for x

Subtract 15 from both sides: $119−15 = 8x$, so $104 = 8x$. Divide both sides by 8, we get $x = 13$.

Step4: Find the length and width

Length $l=5x + 10=5\times13 + 10=65 + 10=75$ feet. Width $w=3x + 5=3\times13+5 = 39 + 5=44$ feet.

Answer:

C. Length = 75 ft, Width = 44 ft