Question

use the information given below to drag the correct answer to each problem to the white box. the perimeter of the rectangle below is 94 units. a which equation could be used to find the value of x? 11.5x + 1 = 94 23x + 2 = 94 33x - 3.75 = 94 b which of the following is the correct value of x? x = 4 x = 2 x = 8 c what are the dimensions of the rectangle? 42.5 by 50.5 9.5 by 14.5 20.5 by 26.5 5.5x - 1.5 6x + 2.5

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=6x + 2.5$ and $w = 5.5x-1.5$, and $P = 94$. So $P=2((6x + 2.5)+(5.5x-1.5))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(6x + 2.5)+(5.5x-1.5)=6x+5.5x+2.5 - 1.5=11.5x + 1$. Then $P = 2(11.5x + 1)=23x+2$. Since $P = 94$, the equation is $23x + 2=94$.

Step3: Solve the equation for x

Subtract 2 from both sides of the equation $23x+2 = 94$: $23x=94 - 2=92$. Then divide both sides by 23: $x=\frac{92}{23}=4$.

Step4: Find the dimensions of the rectangle

Substitute $x = 4$ into the expressions for length and width. Width: $5.5x-1.5=5.5\times4-1.5=22 - 1.5 = 20.5$. Length: $6x + 2.5=6\times4+2.5=24 + 2.5=26.5$.

Answer:

A. $23x + 2=94$
B. $x = 4$
C. $20.5$ by $26.5$