ohh mathh! help?

Question

Bob wants to build a single story house on a piece of property that he is going to purchase. He wants the property to be twice as long as it is wide and he wants a uniform 20 foot clearance on all sides of the house between the house and the property lines. He would also like his house to have an area of 3,000 sq ft. Find the dimensions of the lot that he needs to purchase to build this house.

The equation for this problem is:
(x-40)(2x-40)=3,000

1.) Explain where (x-40) and (2x-40) cme from in this situation
2.)Explain why the product of these must equal 3,000

Solve this problem algebrically, using FACTORING.

Please show me .thank you soo much, all you guys are amazing.

Answer 1

1) let x = width of the lot
then 2x = length of the lot
x - 2*20 = x - 40 = width of the house
2x - 2*20 = 2x - 40 = length of the house

2)The area of the house must then be
(x - 40)(2x - 40) = 3,000 ft^2

Solving:
First, expand the multiplication:
2x^2 - 40x - 80x + 1,600 = 3,000
Collect like terms:
2x^2 - 120x - 1,400 = 0
Factor out the 2:
x^2 - 60x - 700 = 0
(x + 10)(x - 70) = 0
x = - 10, 70
The width of the lot cannot be negative, so it must be 70 ft.
The length of the lot is then 140 ft.

The house measures
30 ft. x 100 ft.

Answer 2

for this problem the x would represent the with and the 2 x would represent the length the 40s r in there because of the clearance needed on each side of the house inbetween the property lines and there are two lengths and two widths so it would be 2 times 20 which equals 40 that is the (x-40)(2x-40) part. . . the 3000 would be the sq footage of the house that he wanted because that would need to be the product of the length and the width of the house as you shouldve learned when you learned area. . . . . . . soooo it goes to 2x^2+1600=3000 then 2x^2=1400 then x^2=700 then x= the squareroot of 700 which is approx. 26.46 sooooo

length = 2 squareroots of 700 or about 52.92
width = the squareroot of 700 which is approx. 26.46 sooooo

youre welcome

Answer 3

1.) (x-40) is the one side of the structure which has 2-20 foot clearanceon both ends, and (2x-40) is the other side which has twice the lenght of the one side of the structure with the 2-20 foot clearance on both ends.

2.) Solving the equation to explain,
(x-40)(2x-40)=3,000.
2xsq. -120x +1,600=3,000
simplipying;
xsq -60x +800 =1,500
xsq -60x -700 =0
by quadratic equation;
b= could not put the equation into motion here but if you know the quadratic equation, you'll get the answer. a=1, b=60 and c=700

Answer 4

1) x is the width of the lot and 2x is the length of the lot
He wants 20 ft of space on each side of the house

Therefore, the width has to be x-40 to allow 20 ft on each side
The length would be 2x-40 to allow 20 ft on each end of the length, also

2) The product of the 2 must be 3000, the area of the house

2x^2-40x-80x+1600=3000 subtract 3000 from both sides

2x^2-120x-1400=0
2(x^2-60x-700)=0 factors of 700 70,10
2(x-70)(x+10) =0
set each factor =0

x-70=0 and x+10=0
x=70 x= -10 (x can't =-10


Therefore, x=70
70-40= 30 ft wide 2(70) =60 ft wide for the house

The lot itself would be 70 ft wide and 100 ft long.

Answer 5

x= how wide the house is

x-40 is because you have 20 foot clearance on each width

2x-40 because the lengths is twice the width and has 20 foot clearance on each length

and it equals 3000 because he has an area of 3000 feet