GMAT数学题求教 （貌似要解1元2次方程）The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkw

GMAT数学题求教 （貌似要解1元2次方程）The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkw
GMAT数学题求教 （貌似要解1元2次方程）
The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?
A.\x0556
B.\x0564
C.\x0568
D.\x0581
E.\x05100
1元2次方程不太会解了 解了半天没解出来 请说明过程 谢谢.

GMAT数学题求教 （貌似要解1元2次方程）The figure shows a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkw
英语好有优势啊 设宽x 中间的正方形长x+5 可列出方程（2x+x+5）平方-（x+5）平方=132
化简得 2x方+5x-33=0 因式分解 （2x+11）（x-3）=0
x1=-5、5「舍去」 x2=3符合
所以小正方形边长8米
所以面积64 选b 打字不容易

设大正方形边长A，小正方形（patio）边长B
A-B=2x= the width of the walkway
the area of the walkway is 132 square meters：132=A平方-B平方=2Ax+2Bx-------①
the width of the patio is 5 meters greater than the width ...

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设大正方形边长A，小正方形（patio）边长B
A-B=2x= the width of the walkway
the area of the walkway is 132 square meters：132=A平方-B平方=2Ax+2Bx-------①
the width of the patio is 5 meters greater than the width of the walkway：B-x=5
A=3x+5 B=x+5 代入①
得A和B
the area of the patio=B的平方

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A.64
x=3
大正方形面积是196，边长是14

设X为走道宽度，那么露台就是X+5，庭院长为X+X+（X+5）=3X+5
如题可得，
(3X+5)x(3X+5)- (X+5)x(X+5)=132
(9XX+30X+25)-(XX+10X+25)=132
合并同类项 8XX+20X=132
16XX+40X=264
16XX+40X+5x5=264+5x5...

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设X为走道宽度，那么露台就是X+5，庭院长为X+X+（X+5）=3X+5
如题可得，
(3X+5)x(3X+5)- (X+5)x(X+5)=132
(9XX+30X+25)-(XX+10X+25)=132
合并同类项 8XX+20X=132
16XX+40X=264
16XX+40X+5x5=264+5x5
(4X+5)x(4X+5)=289
4X+5=17
X=3
那么庭院的面积是(3+5)x(3+5)=8x8=64

B.64

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