Can someone please help me with my math problem?
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Can someone please help me with my math problem?

[From: ] [author: ] [Date: 14-01-15] [Hit: ]
(6 + 2sqrt(6))^2. (4 + 2sqrt(6))^2 = 40 + 8sqrt(6)(6 + 2sqrt(6))^2 = 60 + 12sqrt(6) please rate the answer if it helps-Side of the picture : x then the area is x^2 Side of the frame ( x + 2 ), then the area is ( x + 2 )^2 Given : Ap = 2/3 At Then: x^2 = 2/3 ( x + 2 )^2 Multiply by 3, and expand the binomial 3x^2 = 2 ( x^2 + 4x + 4 ) 3x^2 = 2x^2 + 8x + 8 Form a second degree equation x^2 - 8x - 8 = 0 Solve it by formula: 8 +/- SQ ( 8^2 - 4(1)(-8) ) ------------------------------------ = .........
x^2 = 2/3 * (x^2 + 4x + 4) ---> squaring the (x +2) on the right
x^2 = (2x^2 + 8x + 8)/3 ---> distributing the 2 from 2/3
3x^2 = 2x^2 + 8x + 8 ---> mult. both sides by 3
x^2 -8x -8 = 0 ---> subtract 2x^2 + 8x + 8 from both sides

Then you can use the quadratic formula:
x = (8 +- sqrt(64+32))/2

You can throw out the negative option, since you're dealing with length.

x = (8 + sqrt(96))/2
x = (8 + 4sqrt(6))/2
x = 4 + 2sqrt(6)

Check it: The area of the picture, (4 + 2sqrt(6))^2, should be 2/3 of the total area, (6 + 2sqrt(6))^2.

(4 + 2sqrt(6))^2 = 40 + 8sqrt(6)
(6 + 2sqrt(6))^2 = 60 + 12sqrt(6)

please rate the answer if it helps

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Side of the picture : x then the area is x^2

Side of the frame ( x + 2 ), then the area is ( x + 2 )^2

Given : Ap = 2/3 At

Then: x^2 = 2/3 ( x + 2 )^2

Multiply by 3, and expand the binomial

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

3x^2 = 2x^2 + 8x + 8

Form a second degree equation

x^2 - 8x - 8 = 0

Solve it by formula:

8 +/- SQ ( 8^2 - 4(1)(-8) )
------------------------------------ =
............. 2 (1)

8 +/- SQ ( 96 )
---------------------- =
......... 2

= 8 + 4 SQ (6)
------------------- = 4 + 2SQ (6)........ 4 - 2SQ (6) is negative
......... 2

The side of the picture is ( 4 + 2 SQ (6) ) cm
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