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9. The sum of arcas of two different squares is 400 meter?, the difference of its perimeteris 16 meter find the length of sides of both the squares. |
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Answer» Let side of first square be x and the side of another square be y.difference in perimeter of twosquares:-4x-4y=164(x-y)=16x-y=16/4therefore, x-y=4and x=4+y---take this(1)sum ofareas of two squares:-x²+y²=400Put (1) here(4+y)²+y²=400(4)²+(y)²+2×4×y+y²=40016+y²+8y+y²=4002y²+8y+16-400=02y²+8y-384=02(y²+4y-192)=0 (here we have taken 2 common and take to another side. then it becomes:-)y²+4y-192=0we have done with factorisation method:-y²-12y+16y-192=0y(y-12)+16(y-12)=0(y+16) (y-12)=0either:- | or:-y+16=0 | y-12=0y=-16 | y=12 we will take y=12 because y being side cannot be negative.So, y=12put y=12 in (1)x=4+yx=4+12therefore,x=16and hence, Side of first square=x=16and Side of another square= y = 12. |
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