SOLUTION: Please help me solve this problem: A square picture is mounted in a frame 1 cm wide. The area of the picture is 2/3 of the total area. Find the lenght of a side of the pict

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Question 168375: Please help me solve this problem:
A square picture is mounted in a frame 1 cm wide. The area of the picture is 2/3 of the total area. Find the lenght of a side of the picture.

thank you
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x^2=2/3(x+2)^2
x^2=2/3(x^2+4x+4)
x^2=(2x^2+8x+8)/3
3x^2=2x^2+8x+8
3x^2-2x^2-8x-8=0
x^2-8x-8=0
using the quadratic eqationx+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+we get:
x=(8+-sqrt[-8^2-4*1*-8])/2*1
x=(8+-sqrt[64+32]) /2
x=(8+-sqrt96)/2
x=(8+-9.7979589)/2
x=(8+9.7979589)/2
x=17.7979589/2
x=8.898979 ans. for the length of the side of the picture.
Proof:
8.898979^2=2/3(10.898979)^2
79.19182=2/3*118.78774
79.19182=79.19182