Question

Consider a square and a rectangle with equivalent perimeters. Let the side length of the square be represented by x and the length and width of the rectangle be represented by (2x - 3) and (x + 5), respectively. Formulate and solve an equation to find the value of x.

A) x = 4
B) x = 6
C) x = 8
D) x = 10

Answer 1

The correct answer is option B, x = 6. The question was solved by equating the perimeter of the square to the perimeter of the rectangle and simplifying the resulting equation.

Step-by-step explanation:

The correct answer is option B, x = 6. To solve for x, we start with the perimeter of a square, which is four times the side length, so for the square, the perimeter is 4x. For the rectangle with length (2x - 3) and width (x + 5), the perimeter is 2(2x - 3) + 2(x + 5). Since the perimeters are equal, we can set these two expressions equal to each other:

4x = 2(2x - 3) + 2(x + 5)

Simplifying the equation, we get:

4x = 4x - 6 + 2x + 10

0 = 2x + 4

Dividing both sides by 2, we find:

x = 6

This indicates that the side length of the square is 6 units, which matches option B.

To solve this problem, we need to set up an equation using the information given. The perimeter of a square is given by 4 times the length of one side. So, the perimeter of the square is 4x. The perimeter of the rectangle is given by 2 times the sum of its length and width. So, the perimeter of the rectangle is 2((2x - 3) + (x + 5)). Since the perimeters of the square and rectangle are equivalent, we can set up the equation.

4x = 2((2x - 3) + (x + 5))

Simplifying the equation, we get:

4x = 2(3x + 2)

4x = 6x + 4

2x = 4

x = 2