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: Let the side length of the bare canvas be \(x\) cm.

The side length of the framed painting is \((x + 4+4)=(x + 8)\) cm.

Step2: Use the area formula for a square.

The area of a square is \(A = s^{2}\), where \(s\) is the side - length. Given that the area of the framed painting \(A=625\) square centimeters. So, \((x + 8)^{2}=625\).

Step3: Solve the equation \((x + 8)^{2}=625\).

Take the square root of both sides: \(x + 8=\pm\sqrt{625}\). Since \(x+8>0\) (length cannot be negative), \(x + 8 = 25\).

Step4: Solve for \(x\).

Subtract 8 from both sides: \(x=25 - 8\).

Answer:

A. 17 centimeters