*Question by vluenvy*: 8×10 photograph and frame. Find x.?

Suppose that we have an 8×10 cm photograph which is surrounded by a frame of uniform width x. If the area of the frame is equal to the area of the photograph, what is X?

i tried it like 20 times, each time the answer doesnt fit. help please.

**Best answer:**

*Answer by bpascal*

First, the area of the photograph is 80 cm^2, so this must be the area of the frame as well.

Second, draw a diagram of the photograph surrounded by the uniform thickness frame and label the thickness x.

If we look at the diagrams dimensions including the frame we have

(8 + 2x) X (10 + 2x) and this total area must equal 2 times 80, since we have the photograph and frame area together. So,

(8 + 2x)(10 + 2x) = 160

4x^2 + 36x + 80 = 160

4x^2 + 36x – 80 = 0

x^2 + 9x – 20 = 0

x = [-9 +- sqrt(161)] / 2

The solution with the negative sqrt will be extraneous since x must be positive.

**Give your answer to this question below!**

Since the photograph is 8×10, the frame is (8+x) times (10+x). The value of x represents the wooden frame that covers the photograph.

Area of frame is really the area covered by x and is

(8+2x)(10+2x) – 80 = 36x+4x^2.

Equate this to 80 and you get

4x^2+36x – 80 = 0 which can be solved for x. I got 1.84 as one of the answers for x.