Question

The length of a rectangle is 2 feet more than 3 times the width. If the area is 56 square feet, find the width and the length.

Answer 1

You need the basic area formula for a rectangle to do this. What is the area of a rectangle?

Answer 2

A=LW

Answer 3

Good! So let's draw a picture:

Answer 4

Now, it looks like this:Can you do that math?

Answer 5

\[59=2x+3x ^{2}\]
\[0=2x+3x^2-59\]
this is what i have so far...

Answer 6

Yes! I am so glad to see that you knew to move the 59 over. Now this is a polynomial of second degree that you should be able to factor when you rearrange the terms like this:\[3x ^{2}+2x-59=0\]See if you can factor that. Me, I'd try the quadratic formula first thing; it's easier to find the zeros that way.

Answer 7

How did you do? Did you find the dimensions?

Answer 8

every time i factor i get fractions....

Answer 9

Let me try. Give me a sec. I won't go away til we get this. Ok?

Answer 10

ok. Thank you

Answer 11

Ok, there are actually several different ways you can find the zeros of the polynomial: by completing the square, the quadratic formula, using the Rational Roots theorem or by long division. We will do it the easiest way for you and pick the quadratic formula. Assuming you know the formula, I am just going to post it with the coefficients in it. Ok?

Answer 12

\[\frac{ -2\pm \sqrt{4-4(3)(-56)} }{ 6 }\]

Answer 13

That mess simplifies down to\[\frac{ -2\pm \sqrt{4+672} }{ 6 }\]

Answer 14

I don't know how to use the quadratic formula yet..

Answer 15

Which simplifies even further to\[\frac{ -2\pm \sqrt{676} }{ 6 }\]or\[\frac{ -2\pm26 }{ 6 }\]Using those as your possible answers we have 24/6 which is 4.

Answer 16

So the width is 4. NOW...if you don't know the quadratic formula, we can just factor it the regular way. Like this:\[3w ^{2}+2w-56=0-->(x-4)(x+14)\]

Answer 17

You get (w - 4) = 0 and (w + 14) = 0. Solving those for w you get w = 4 and w = -14. We know that a width cannot be a negative number, so the width must be 4. Do you get it?

Answer 18

Thanks I understand it better now. thank you

Answer 19

Good. Now that you know that w = 4, you can find the length by filling 4 into your w in the length expression: L = 2 + 3W-->L = 2 + 3(4)...L = 2 + 12...L = 14

Answer 20

Thank you for the medal!d You upped my SmartScore by one when you did that! : )