Questions: Unproctored Placement Assessment Question 4 The perimeter of the rectangle below is 120 units. Find the length of side AB. Write your answer without variables. AB=

Unproctored Placement Assessment Question 4 The perimeter of the rectangle below is 120 units. Find the length of side AB. Write your answer without variables. AB=
Transcript text: Unproctored Placement Assessment Question 4 The perimeter of the rectangle below is 120 units. Find the length of side $\overline{A B}$. Write your answer without variables. $\square$ \[ A B= \]
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Solution

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Solution Steps

Step 1: Set up an equation for the perimeter.

The perimeter of a rectangle is given by $P = 2(l+w)$, where $l$ is the length and $w$ is the width. In this case, we are given that the perimeter is 120 units. We can label side AB as the length and side BC as the width. Thus, we have the equation: $120 = 2(4x + 5x - 3)$

Step 2: Simplify and solve the equation.

First, combine the x terms inside the parenthesis: $120 = 2(9x - 3)$ Next, distribute the 2: $120 = 18x - 6$ Add 6 to both sides: $126 = 18x$ Divide both sides by 18: $x = 7$

Step 3: Find the length of side AB.

Substitute the value of x back into the expression for the length of side AB, which is $4x$. $AB = 4x = 4(7) = 28$

Final Answer:

28

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