Question

select the correct answer.
a square - shaped canvas painting was enlarged by adding a 4 - centimeter wide decorative frame to the length and width of the canvas. if the area of the framed painting is 625 square centimeters, what is the side length of the bare canvas?
a. 17 centimeters
b. 19 centimeters
c. 21 centimeters
d. 25 centimeters

Explanation:

Step1: Find the side length of the framed painting

Since the area of a square is \(A = s^{2}\), and \(A = 625\) \(cm^{2}\). Then \(s=\sqrt{625}=25\) \(cm\).

Step2: Relate the side length of the framed and bare canvas

Let the side length of the bare canvas be \(x\). The side length of the framed canvas is \(x + 2\times4\) (because the frame is on both sides). So \(x+8 = 25\).

Step3: Solve for \(x\)

Subtract 8 from both sides of the equation \(x+8 = 25\). We get \(x=25 - 8=17\) \(cm\).

Answer:

A. 17 centimeters