作业帮数学,用函数和因式分解 解应用题- 离问题结束还有 14 天 23 小时 A rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4m. The length of the rectangular carpet is 2m less than three time
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数学,用函数和因式分解 解应用题- 离问题结束还有 14 天 23 小时 A rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4m. The length of the rectangular carpet is 2m less than three time
数学,用函数和因式分解 解应用题
- 离问题结束还有 14 天 23 小时
A rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4m. The length of the rectangular carpet is 2m less than three times its width. Find the dimensions of the rectangular carpet
请算出这道题,
数学,用函数和因式分解 解应用题- 离问题结束还有 14 天 23 小时 A rectangular carpet and a square carpet have equal areas. The square carpet has a side length of 4m. The length of the rectangular carpet is 2m less than three time
Solution :
Let the length of rectangular carpet be X,
the width of rectangular carpet be Y.
Area of square carpet = 4×4 = 16
Area of rectangualr carpet = XY = 16
∵ X = 3Y - 2 (Given)
∴ (3Y-2)Y = 16
ie.3Y² - 2Y - 16 = 0
(Y+2)(3Y-8) = 0
∴ Y₁= -2 (Rejected)
Y₂= 8/3 (m)
∴ Y = 8/3,X = 16÷(8/3) = 6 (m)
So,the length and width of the rectangular carpets are 6 m and 8/3 m,respectively.
s=4*4=a*b
a=3b-2
thus,we find 16=b(3b-2)
3b^2-2b-16=0
(3b-8)(b+2)=0
therefore,
b=8/3 a=3b-2=6