Question

using your math 6. a rectangle with a total of 80 square feet has been broken into two rectangles with areas of 56 square feet and 24 square feet as shown. the common length of the two smaller rectangles is a whole number that is greater than either width 1 or width 2, which are both whole numbers. from this information, determine the length, width 1, and width 2. explain how you found your answers.

Explanation:

Step1: Find GCD of 56 and 24

The length is the greatest common divisor (GCD) of 56 and 24. Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. GCD is 8. So length = 8.

Step2: Calculate Width 1

Area of first rectangle = length × width1. So \( 56 = 8 \times \text{width1} \), \( \text{width1} = \frac{56}{8} = 7 \).

Step3: Calculate Width 2

Area of second rectangle = length × width2. So \( 24 = 8 \times \text{width2} \), \( \text{width2} = \frac{24}{8} = 3 \).

Answer:

Length = 8 feet, Width 1 = 7 feet, Width 2 = 3 feet