A picture of a sunset has a square frame that is 2 inches wide. The area of the picture is one-third of the total area of the picture and frame. What are the dimensions of the picture to the nearest quarter of an inch? please show me the steps.

Question

anonymous · Answer

Let's say the side length of the picture is s. The area of the picture would be s^2. The side length of the frame would be (s+2), and its area would be (s+2)^2, obviously. Thus we can set up an equation: s^2=(1/3)(s+2)^2. When you take the square root of each side, you get s=(1/9)(s+2). Distribute to get s=(1/9)s+2/9. subtract (1/9)s from both sides to get (8/9)s=(2/9). Divide each side by 8/9 to get that the side length of the picture is 1/4. Therefore, its area is (1/4)^2 or 1/16 of an inch.

anonymous · Answer

can you try one more time .the answer is 5 and 1/2 in by 5 and 1/2 in. i would like to know how to do it

anonymous · Answer

oh sorry the side length of the frame is s+4

anonymous · Answer

so you plug that in to the equation s^2=(1/3)(s+4)^2 and solve for s! The dimensions will be s by s. :)

anonymous · Answer

thanks