Question

Help! A rectangular plot of land has an area of 512 square feet and is 16 feet longer than it is wide.

-Write a quadratic formula in the form ax^2+bx+c=0 (whose solution is the width of the plot of land)
-Solve the equation

Answer 1

ok, you know that:
`Area of a rectangle = (rectangle's width) • (rectangle's length)`

right?

Answer 2

now, you are also given that your length is 16 feet longer than the width.
So, if you were to name your width - "x",
then your length, which is given to be 16 feet longer than width, will be x+16.

Answer 3

YOu are given the area of this rectangle too. it is 512 (square feet)

Answer 4

So, since:
`Area of a rectangle = (rectangle's width) • (rectangle's length)`

then, therefore:
`512 = (x) • (x+16)`

Answer 5

When you expand that, and subtract 512 from both sides, then you got the quadratic equation in a form that you want.

Answer 6

if you have further questions, ask.

Answer 7

So the formula in the standard form would be (x)*(x+16)-512?

Answer 8

@SolomonZelman

Answer 9

you got so far,
x•(x+16)-512=0

Answer 10

you need to expand the x•(x+16) peace

Answer 11

So by expanding the x*(x+16) piece it would be in its standard form of x^2+16x-512 ? @SolomonZelman

Answer 12

yes

Answer 13

x²+16x-512=0

then sovle for x

Answer 14

factoring or completing the square would be fairly easy, but if you don't know how to do these methods or don't feel like, then you can use the quadratic formula (if you want, just ask, i will post the quadratic formula)