Question

Word problem help?
The length of a rectangle is 3 yd less than twice the width, and the area of the rectangle is 65 yd^2. Find the dimensions of the rectangle.

Answer 1

Ok so what you have here is a system of equations\[l=2w-3\]
and\[lw=65\]
I suggest using substitution and putting in (2w-3) for l in the area equation

Answer 2

I'm not sure I understand.

Answer 3

Well you know that\[l=2w-3\]

Answer 4

Right?

Answer 5

So can't you put in 2w-3 for l in the second equation?
and make it\[w(2w-3)=65?\]

Answer 6

So solve for w?

Answer 7

Yes you are going to have to solve this like a quadratic

Answer 8

w= -5 ?

Answer 9

Well can you have a negative value in a rectangle?
Remember this is a quadratic so I suggest finding the positive zero

Answer 10

I don't know how to do that.

Answer 11

Well -5 was one of the zeroes of the quadratic, how did you get that?

Answer 12

I simplified both sides of the equation, subtracted 65 from both sides, factored out the left side of the equation, and set the factors equal to 0

Answer 13

Ok so what were your two factors?

Answer 14

You're really close

Answer 15

(2w−13)(w+5)=0

Answer 16

Ok so you got -5 by setting w+5 equal to zero

What would you get when you set 2w-13 equal to zero?

Answer 17

13/2

Answer 18

or 6.5

Answer 19

YEP well done :)
So now substitute that either into l=2w-3 or lw=65
and solve for l

Answer 20

so width is 6.5 and length would be 10?

Answer 21

Yep that would be correct
Good job :)