The perimeter of a rectangle with dimensions 4cm by x cm is 18cm greater than that of a square . If the have equal areas, find
(a) the lenght od a side of the square
(b) the value of x
數學文字題
2007-01-09 11:33 pm
回答 (2)
2007-01-09 11:38 pm
✔ 最佳答案
let the lenght of a side of the square is ythen
4x=y^2...(1) (area condition)
2(4+x)=4y+18 (perimeter condition)
8+2x=4y+18
2x=4y+10
x=2y+5...(2)
sub (2) into (1)
4(2y+5)=y^2
y^2-8y-20=0
(y-10)(y+2)=0
y=10 or -2 (rejected)
so
the lenght of a side of the square is 10 cm
(b)
the value of x
=2y+5
=2*10+5
=25
2007-01-09 11:52 pm
let the lenght of a side of the square is y
then
4x=y^2...(1) (area condition)
2(4+x)=4y+18 (perimeter condition)
8+2x=4y+18
2x=4y+10
x=2y+5...(2)
sub (2) into (1)
4(2y+5)=y^2
y^2-8y-20=0
(y-10)(y+2)=0
y=10 or -2 (rejected)
so
the lenght of a side of the square is 10 cm
(b)
the value of x
=2y+5
=2*10+5
=25
then
4x=y^2...(1) (area condition)
2(4+x)=4y+18 (perimeter condition)
8+2x=4y+18
2x=4y+10
x=2y+5...(2)
sub (2) into (1)
4(2y+5)=y^2
y^2-8y-20=0
(y-10)(y+2)=0
y=10 or -2 (rejected)
so
the lenght of a side of the square is 10 cm
(b)
the value of x
=2y+5
=2*10+5
=25
收錄日期: 2021-04-25 16:50:19
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