Question

The perimeter of the rectangle below is 42 inches. Set up an equation and solve. The length is 5x, and the width is x-3.

a. 2(5x + x-3) = 42; x = 6
b. 2(5x + x-3) = 42; x = 5
c. 2(5x + x-3) = 42; x = 7
d. 2(5x + x-3) = 42; x = 8

Answer 1

To solve for x in the equation 2(5x + x-3) = 42, we can simplify the equation and isolate x. The value of x in this case is 8, making option d the correct answer.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to add up the lengths of all four sides. The length of the rectangle is given as 5x and the width is x-3. Since the perimeter is the sum of all four sides, we can set up the equation 2(5x + x-3) = 42. To solve for x, we can distribute the 2 and then combine like terms: 10x + 2x - 6 = 42. Simplifying further, we get 12x - 6 = 42. Adding 6 to both sides, we have 12x = 48. Finally, dividing both sides by 12, we find x = 4. Thus, option d. 2(5x + x-3) = 42; x = 8 is the correct answer.