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1. The length of a rectangle is 13 cm more than the width. The perimeter is 44 cm. Find the length and width.

2. The perimeter of a rectangle is 124 meters. The length is 7 meters more than twice the width. What are the dimensions of the rectangle?

3. The length of a rectangle is 9 meters less than three times its width. The perimeter is 86 meters. Find the length and width.

4. Side A of a triangle is 4 cm longer than side B. Side B is twice as long as side C. What is the length of each side if the triangle’s perimeter is 28 cm?

5. The two longest sides of a pentagon are each 3 times as long as the shortest side. The other two sides are each 5 meters longer than the shortest side. Find the length of each side if the perimeter of the pentagon is 105 meters.

6. The lengths of the sides of a triangle are \(x+2\), \(x+4\), and \(x+6\). If the perimeter of the triangle is 78 cm, what is the value of \(x\)? What are the lengths of all the sides?

7. The length of a triangle is three consecutive odd integers. The perimeter of the triangle is 57 cm. What is the length of the longest side of the triangle? What are the lengths of the other two sides?

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Do you want a detailed solution for any specific problem, or should I solve them all? Let me know! Here are 5 additional questions that could be of interest:

1. How do you solve for the perimeter of a triangle given different expressions for each side?
2. What is the general formula for the perimeter of a rectangle?
3. How can the concept of consecutive integers be applied to geometry problems?
4. How does one set up an equation for problems involving dimensions like length and width?
5. What is the relationship between the sides and perimeter of a pentagon?

**Tip**: Always start by expressing unknowns in terms of variables and set up equations based on given conditions for perimeter or area.

The math problems involving geometry concepts such as rectangles, triangles, and pentagons with a focus on perimeter and side length calculations.

Solve geometry problems involving the perimeter of rectangles, triangles, and pentagons. This guide walks through calculations using algebraic expressions for side lengths and perimeters. Suitable for students in Grades 6-8.

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