Question

I NEED HELP ASAP. I AM CURRENTLY 6 LESSON DAYS BEHIND AND VERY DEPRESSED/STRESSED!!
You are making a rectangular table. The area of the table should be 10 ft^2. You want the length of the table to be 1 ft shorter than twice its width. What should the dimensions of the table be?

Okay, so, I'm not sure how to put this into an equation. The example in the book is very different to this problem.

Answer 1

let w = width

"You want the length of the table to be 1 ft shorter than twice its width"

so the length is 2w-1

Answer 2

Area = Length * Width

A = L*W

10 = (2w-1)*w

10 = w*(2w-1)

10 = 2w^2 - w


agreed so far?

Answer 3

Yeah

Answer 4

get everything to one side

10 = 2w^2 - w

10-10 = 2w^2 - w - 10

0 = 2w^2 - w - 10

2w^2 - w - 10 = 0

Answer 5

to solve 2w^2 - w - 10 = 0, you can factor but using the quadratic formula is the best option

Answer 6

Yeah, we're currently using quadratic formulas.

Answer 7

2w^2 - w - 10 = 0

means

a = 2
b = -1
c = -10

plug those values of a,b,c into the quadratic formula

Answer 8

2x^2+-x+-10=0
Like that?

Answer 9

yes you can swap each w for x

Answer 10

and rewrite it like that, yep

Answer 11

Okay, thank you very much! I've pretty much got everything from here. ;D

Answer 12

you're welcome

Answer 13

Let me show you how to find the solutions using the quadratic formula

Answer 14

Quadratic Formula:

\[\Large x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 15

a = 2
b = -1
c = -10


\[\Large x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
\[\Large x=\frac{-(-1) \pm \sqrt{(-1)^2-4*(2)*(-10)}}{2*(2)}\]
\[\Large x=\frac{1 \pm \sqrt{81}}{4}\]
\[\Large x=\frac{1 + \sqrt{81}}{4} \text{ or } x=\frac{1 - \sqrt{81}}{4}\]
\[\Large x=\frac{1 + 9}{4} \text{ or } x=\frac{1 - 9}{-2}\]
\[\Large x=\frac{10}{4} \text{ or } x=\frac{-8}{4}\]
\[\Large x=\frac{5}{2} \text{ or } x=-2\]
\[\Large x=2.5 \text{ or } x=-2\]

Answer 16

Yeah, that is what the algebra calculators said too but for some reason, the back of the book says the answer is 2.5 ft by 4 ft, which is what makes me so confused.

Answer 17

well x = -2 is tossed out because we can't have a negative width

Answer 18

x = 2.5 is the only possible width

Answer 19

x = width

""You want the length of the table to be 1 ft shorter than twice its width""

so length = 2x - 1

Answer 20

length = 2x - 1

length = 2*2.5 - 1

length = 4

Answer 21

Ooh, thanks so much!! ;'D