Let the width of the rectangle be denoted as \( w \) (in cm). According to the problem, the length of the rectangle is \( l = w + 10 \) cm.
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2l + 2w \]
Substituting the expression for length into the perimeter formula gives:
\[ P = 2(w + 10) + 2w \]
Simplifying this:
\[ P = 2w + 20 + 2w = 4w + 20 \]
We know that the perimeter is more than 100 cm, so we can set up the inequality:
\[ 4w + 20 > 100 \]
Now, let's solve the inequality:
- Subtract \( 20 \) from both sides:
\[ 4w > 100 - 20 \] \[ 4w > 80 \]
- Divide both sides by \( 4 \):
\[ w > \frac{80}{4} \] \[ w > 20 \]
Thus, the width \( w \) must be greater than \( 20 \) cm.
Conclusion
The inequality that represents the situation is \( 4w + 20 > 100 \), and the solution is \( w > 20 \) cm. This implies that the width of the rectangle must be more than 20 cm.
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