Can someone please help me with my math problem?

The entire area = (x + 2)^2
2/3(x + 2)^2 = x^2 Multiply by = 3
2(x + 2)^2 = 3x^2 Expand the brackets
2(x^2 + 4x + 4) = 3x^2 Remove the brackets.
2x^2 + 8x + 8 = 3X^2 Bring the left side from the right side.
0 = x^2 - 8x - 8



Use the quadratic formula to get the value of x.
a = 1
b = - 8
c = - 8

x = [-b +/- sqrt(b^2 - 4ac)] / (2a)
x = [- (-8) +/- sqrt( (-8)^2 - 4*(1)*(-8)] / (2*1)
x = [ 8 +/- sqrt(64 + 32) ] / 2
x = [8 +/- sqrt(96)] / 2
x = [8 +/- 4sqrt(6) ]/2
x = 4 +/- 2*sqrt(6)
x1 = 8.899
x2 = -0.899 This value does not work.

Check
=====
(x + 2)^2 = (8.898+2)^2 = 10.898^2 = 118.79
x^2 = 8.899^2 = 79.19

Now is 2/3 * 118.79 close to 79?
Try it. 2/3 * 118.79 = 79.19 which is good enough.

x^2 = (2/3)(x + 2)^2 gives x^2 -- 8x -- 8 = 0 whence x = 4 +/-- 2sqrt(6)
giving side of picture = 4 + 2sqrt(6) cm ANSWER

The area of the picture is x^2.

The total area is (x + 1)^2. So the problem says

x^2 = (2/3)(x + 1)^2

3x^2 = 2(x^2 + 2x + 1) = 2x^2 + 4x + 2

x^2 - 4x - 2 = 0. Now use the quadratic formula, and the positive solution is

x = 2 + √6 cm

Let x be the length of a side of the picture. Then x^2 is the area of that picture. The total area is (x + 2)^2, since there's one inch of frame on each side of the picture. So, you have x^2 = 2/3 * (x + 2)^2.

Then you can do some algebra: