Let's break down the rectangle word problem from the image and solve it step by step:

Given Information:

• Length of the rectangle: Two times the width increased by 5 cm.
• Perimeter of the rectangle: 46 cm.

Step 1: Define variables.

Let:

• $w$ be the width of the rectangle.
• The length of the rectangle is given as $2w + 5$ (two times the width plus 5 cm).

Step 2: Use the perimeter formula for a rectangle.

The perimeter $P$ of a rectangle is given by: $P = 2 \times (\text{length} + \text{width})$

Substituting the given perimeter (46 cm) and the expressions for length and width: $46 = 2 \times \left( (2w + 5) + w \right)$

Step 3: Simplify and solve for $w$.

First, simplify the expression inside the parentheses: $46 = 2 \times (3w + 5)$ Next, distribute the 2: $46 = 6w + 10$ Subtract 10 from both sides: $36 = 6w$ Divide both sides by 6: $w = 6$

Step 4: Find the length.

Now that we know the width $w = 6$, substitute this into the expression for the length: $\text{Length} = 2w + 5 = 2(6) + 5 = 12 + 5 = 17$

Final Answers:

• Width: 6 cm
• Length: 17 cm

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What would the perimeter be if the width were doubled?
2. If the width were 8 cm, what would the new length be?
3. How would the area of the rectangle change if the perimeter were 60 cm?
4. What is the area of the rectangle given the width and length we calculated?
5. How would you set up the equation if the length was 3 times the width instead of 2 times plus 5 cm?

Tip: Always double-check your setup by plugging the values back into the original problem to confirm that the conditions are met (e.g., checking the perimeter calculation).