Question

the figure is made up of two identical squares and has a perimeter of 42 inches. what is the area of one square?

Explanation:

Step1: Analyze the perimeter formula

Let the side - length of each square be \(x\) inches. When two identical squares are joined, the perimeter of the new figure is composed of 6 sides of the square. So, the perimeter \(P = 6x\).
Given \(P=42\) inches, we have the equation \(6x = 42\).

Step2: Solve for the side - length

Solve the equation \(6x = 42\) for \(x\). Divide both sides of the equation by 6: \(x=\frac{42}{6}=7\) inches.

Step3: Calculate the area of one square

The area formula of a square is \(A=x^{2}\). Substitute \(x = 7\) into the formula: \(A=7^{2}=49\) square inches.

Answer:

49