Determine the width of a frame.

Question

A rectangular painting measures 10 inches by 14 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by painting and its frame is 64 inches.

Answer 1

Call the width w.

 

The dimensions of the painting and the frame are 10 + 2w by 14 + 2w.  It's 2w in both cases because the frame is on both the top and the bottom, and the left and the right, of the painting.

 

The perimeter is 2(10 + 2w) + 2(14 + 2w) = 20 + 4w + 28 + 4w = 48 + 8w.

 

We know that's equal to 64 inches, so that gives us an equation:

 

48 + 8w = 64

8w = 16

w = 2 inches

 

 

Answer 2

Kathrine,

The inner rectangle is 10 by 14. That means the outer rectangle has to be (l=10+2x) by (w=14+2x), x being the width of the frame.

The perimeter of the frame, p = 2l + 2w = 2(10+2x) + 2(14+2x) = 64

<=> (10+2x) + (14+2x) = 32

<=> (10+14) + (2x+2x) = 32

<=> 4x = 32 - 24

<=> 4x = 8,

The width of the frame, x = 2 inches

Answer 3