Solve the problem.
-A rectangular plot has area $126 \mathrm { yd } ^ { 2 }$ with a perimeter of $46 \mathrm { yd }$. What is the length of the longest side?
A) $13 \mathrm { yd }$
B) $12 \mathrm { yd }$
C) $16 y d$
D) $14 \mathrm { yd }$

Question

Quizplus · Accepted Answer

The area of a rectangle is given by $A = l \times w$, where $l$ is the length and $w$ is the width. The perimeter of a rectangle is given by $P = 2l + 2w$. Given $A = 126 \, \text{yd}^2$ and $P = 46 \, \text{yd}$, we can set up the equations: $l \times w = 126$ and $2l + 2w = 46$. Simplifying the perimeter equation gives $l + w = 23$. To find the dimensions that satisfy these conditions, we can factor 126 to find pairs of factors that sum to 23. The pair that fits is $14$ and $9$, where $14 \, \text{yd}$ is the length and $9 \, \text{yd}$ is the width. Therefore, the length of the longest side is $14 \, \text{yd}$.

Solve the Problem 126yd2126 \mathrm { yd } ^ { 2 }126yd2

Solve the Problem $126 \mathrm { yd } ^ { 2 }$