SOLUTION: A wire of length 200 cm is cut in to two parts and each part is bent to form a square . If the area of the larger square is 9 times that of the smaller square , find the perimeter

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Question 964079: A wire of length 200 cm is cut in to two parts and each part is bent to form a square . If the area of the larger square is 9 times that of the smaller square , find the perimeter of the larger square.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
L=side of large square; S=side of small square
4L%2B4S=200cm
L%2BS=50cm
L=50cm-S Use this to substitute for L.
L%5E2=9S%5E2 Substitute for L.
%2850cm-S%29%5E2=9S%5E2
2500-100S%2BS%5E2=9S%5E2 Subtract S^2 from each side.
2500-100S=8S%5E2 Add 100S to each side.
2500=8S%5E2%2B100S Subtract 2500 from each side.
0=8S%5E2%2B100S-2500
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B100x%2B-2500+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28100%29%5E2-4%2A8%2A-2500=90000.

Discriminant d=90000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-100%2B-sqrt%28+90000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28100%29%2Bsqrt%28+90000+%29%29%2F2%5C8+=+12.5
x%5B2%5D+=+%28-%28100%29-sqrt%28+90000+%29%29%2F2%5C8+=+-25

Quadratic expression 8x%5E2%2B100x%2B-2500 can be factored:
8x%5E2%2B100x%2B-2500+=+8%28x-12.5%29%2A%28x--25%29
Again, the answer is: 12.5, -25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B100%2Ax%2B-2500+%29

S=12.5 cm
L=50cm-12.5cm=37.5cm
ANSWER: Perimeter of large square=4(37.5cm)=150 cm
CHECK:
L%5E2=9S%5E2
37.5%5E2=%289%29%2812.5%5E2%29
1406.25=%289%29%28156.25%29
1406.25=1406.25