length and width

Question

The length of a painting is 2 inches longer than the width. The area of the painting is 48in^2. If a 3-inch frame is put around the painting, what is the area of the frame?

 

Answer 1

Use the area of the painting, you should be able to figure out the length and width of the painting.  

To find the area of the frame, you will need to find the area of frame + painting - painting

 

Given: L_P = 2 + W_P, A_P = 48

A_P = L_P * W_P

Substitute the first equation in the second equation

48 = (2 + W_P) * W_P

48 = 2W_P + W_P²

0 = W_P² + 2W_P - 48

W_P = {6, -8},  can't have negative number, so W_P = 6 inches

 

Substitute back to the first equation, L_P = 2 + 6 = 8 inches

 

To have a frame of 3 inches all around...L_F = 8 + 6 = 14 inches, W_F = 6 + 6 = 12 inches

Area of the frame with the painting: A_F = L_F * W_F = 14 * 12 = 168 inches²

Just the frame = 168 - 48 = 120 inches²