Width - Driveway

Imagine that the driveway is made up of 3 separate areas. 1 long drive down each side of the property and a shorter drive at the rear of the property which links those 2 long drives.

Let the width of each drive equal the unknown variable 'x' . Calculate the area of one long drive (clue the answer is 100x), add the area of the other long drive, calculate and add the area of the shorter drive at the back of the property. The sum of the 3 drive areas is a quadratic equation.

Solve the quadratic equation.

I am guessing:

The front of house is: Driveway - House - Driveway

Width - House - Driveway 100 (Front of House) - 2x

Side of House - Driveway 100 (Side of House) - x

(100 - 2x) (100 - x) Area= Length x Width

10000 - 100x - 200x - 2x^2

??

The drive down each side of the property has width 'x' and length 100 for an area of 100x each.

The short drive at the back has width 'x' and length '100-2x' for an area of 100x-2x^2.

The total drive 5000= 100x +100x +100x-2x^2

Combine like terms and solve the equation.

5000 = 100x + 100 x + 100x - 2x^2
5000 = 300x - 2x^2

I am not sure from here- not good at quadratics.

Rearrange into a quadratic equation then solve using the formula or go to the website calculator.

"If you have an equation of the form "ax^2 + bx + c = 0", we can solve it for you.
Just enter the values of a, b and c below."



http://www.mathsisfun.com/quadratic-equation-solver.html

I don't understand.

To re-arrange 5000 = 300x - 2x^2 into a quadratic equation you do the same thing to both sides of the equation which leaves it unchanged but in a form suitable to solving using a formula. Subtract 300x and add 2x^2 to both sides of the equation which describes the area of the drive way to obtain:

2x^2 -300x +5000 = 0

This is a quadratic equation in the form:


ax^2 + bx + c = 0

Note that the two roots of a quadratic equation in this form can be solved using the formula :



If using the formula for the solution to the equation (namely the two roots of the equation equal to 'x') is too onerous then use the calculator website below which does it more quickly.

http://www.mathsisfun.com/quadratic-equation-solver.html

Let me know what you discover.

Using the equation solver:
-130
-19

I haven't used the formula.

Formula:

X = -b + - sq. root b^2 - 4ac / 2a

X = 300 + - 300^2 - 4(2) (5000) / 2(2)

X = 300 + - 90000 - 8 (5000) / 4

X = 300 + - 90000 - 40000 / 4

X = 300 + - 50000 / 4

X = 300 + - 50000 /4 = 223.60 / 4

X = 300 - 223.60 / 4 = 19.1

X = 300 + 223.60 / 4 = 130.9

??

I haven't observed a driveway wider than a house. If the answer is correct, 19.1 is width.

What are dimensions of house? Just curious.

If you think that is curious check this out:

If the equation 2x^2 -300x +5000 = 0 is divided by 2 on both sides it is unchanged in its equivalence so:

x^2 -150x +2500 = 0

The sum of the roots of the equation you calculated is 150 (130.9 + 19.1) .
The product of the roots of the equation you calculated is 2500 (130.9 x 19.1 ).

I will leave you to calculate the dimensions of the house (but I'm guessing the area is 5000 ) and to think about why 19.1 is the only possible answer.

I don't know about the house dimensions.

You know that the land is 100 x 100 and that the drive is 19.1 wide down one side , at the back , and up the other side.

Subtraction of the dimensions of the drive from the dimensions of the land allows the house dimensions to be calculated.

19.1 +19.1 + 19.1 = 57.3
100 * 100 = 10000

10000 - 57.3 = 9942.7 = 9948 sq. ft.

??

Should be 9943

The land is 100 feet wide so the house is 61.8 feet wide :

I<<<< 19.1 >>>>I<<<<<<<<<<< 61.8 >>>>>>>>>>>I<<<< 19.1 >>>>I
DRIVEWAY.......I...................... HOUSE .....................I......DRIVEWAY


The land is 100 feet long so the house is 80.9 feet long because the driveway at the back of the property is 19.1 feet.

Thanks.