Alg3.2.17

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If twice the area of a smaller square is subtracted from the area of a larger square,the result is 14 square cm.However,if the twice the area of the larger square is added to three times the area of the smaller square,the result is 203 square cm.Determine the sides of the two squares.

Let the area of the smaller square be x^2\,

From the first given condition,area of the larger square is x^2+14\,

As per the second condition

2(x^2+14)+3x^2=203\,

5x^2+28=203,5x^2=175,x^2=25,x=5\,

The area of the larger square is 5^2+14=39\,

Side of the larger square is \sqrt{39}\, cm.

Side of the smaller square is 5\, cm.


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