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The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length (l) and width (w) of the pool?

A.
[tex]\[
\begin{aligned}
w & \leq l - 10 \\
2l + 2w & \geq 62
\end{aligned}
\][/tex]

B.
[tex]\[
\begin{aligned}
w & \leq l - 10 \\
2l + 2w & \ \textgreater \ 62
\end{aligned}
\][/tex]

C.
[tex]\[
\begin{aligned}
w & \leq 10 - l \\
2l + 2w & \geq 62
\end{aligned}
\][/tex]

D.
[tex]\[
\begin{aligned}
w & \leq 10 - l \\
2l + 2w & \ \textgreater \ 62
\end{aligned}
\][/tex]

Sagot :

GinnyAnswer
To find a system of inequalities representing the possible length (let’s denote it as [tex]\( l \)[/tex]) and width (let’s denote it as [tex]\( w \)[/tex]) of a rectangular pool, we need to consider the following conditions given in the problem:

1. The perimeter of the rectangular pool is more than 62 meters.
2. The width is at least 10 meters less than the length.

First, we translate these conditions into mathematical inequalities.

### Step 1: Perimeter Constraint
The perimeter [tex]\( P \)[/tex] of a rectangle is given by the formula:
[tex]\[ P = 2l + 2w \][/tex]
According to the problem, the perimeter must be more than 62 meters:
[tex]\[ 2l + 2w > 62 \][/tex]

### Step 2: Width Constraint
It is also given that the width [tex]\( w \)[/tex] is at least 10 meters less than the length [tex]\( l \)[/tex]. This translates to:
[tex]\[ w \leq l - 10 \][/tex]

### System of Inequalities
Combining these two constraints, we get the following system of inequalities:
[tex]\[ \begin{aligned} 2l + 2w & > 62, \\ w & \leq l - 10. \end{aligned} \][/tex]

These inequalities represent the possible values for the length [tex]\( l \)[/tex] and width [tex]\( w \)[/tex] of the rectangular pool.
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