SOLUTION: Farmer Bob would like to plant six additional fields of produce in another part of his property. Find the dimensions of each field, in terms of x, given their area.
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Question 1164439: Farmer Bob would like to plant six additional fields of produce in another part of his property. Find the dimensions of each field, in terms of x, given their area.
Strawberry field with area 16x2+4x
A= L x W
16x^2+4x=L x W
16x^2+4x= 4x(4x+1)
L= 4x+1
W=4x
Cucumber field with area x2-4x-21
A= L x W
x^2-4x-21=L x W 21=7x3
x^2-7x+3x-21= L x W
(x^2-7x)+(3x-21)= L x W
x(x-7)+3(x-7)=L x W
(x-7)(x-3) = L x W
L= x-7
B=x-3
Tomato field with area x2-36
A=L x W
a^2-b^2=(a+b)(a-b)
x^2-36=L x W
x 6
(x+6)(x-6)= L x W
L=x+6
W=x-6
Parsley field with area x2-10x+21
A=L x W
x^2-10x+21=L x W 21=3x7
x^2-3x-7x+21=L x W
(x^2-3x)-(7x+21)=L x W
x(x-3)-7(x-3)=L x B
(x-3)(x-7)=L x B
L=x-3
W=x-7
Onion field with area x2-11x+30
A=L x W
x^2-11x+30=L x W 30=6x5
x^2-6x-5x+30=L x W
(x^2-6x)-(5x+30)=L x W
x(x-6)-5(x-6)=L x W
(x-5)(x-6)=L x W
L=x-5
W=x-6
Watermelon field with area x2+8x-20
A=L x W
x^2+8x-20=L x W 20=10x2
x^2+10x-2x-20=L x W
(x^2+10x)-(2x-20)=L x W
x(x+10)-2(x+10)=L x W
(x+10)(x-2)=L x W
L=x+10
W=x-2
What values of x cannot be used if the above six fields are to be built together? Answer by ikleyn(52847) (Show Source):
