I need help finding the length of a rectangle...

Question

The length of a rectangle is 3 cm greater than the width of the rectangle. If the area of the rectangle is 40 square cm, what is the length of the rectangle?

I'm having trouble doing my Algebra work and the video doesn't help me. Can someone explain properly how to do this?

Answer 1

Hi Christian!

Area = Length x Width

Where:

Length = L

Width = W

Area = 40 cm²

And you know that 

L: W + 3

Therefore

40 cm² = L x W

Or

40 cm² = (W+3)(W)

Combining the L x W you get

40 cm^2 = (W²)+3W

This is almost in a format we can use for the Quadratic formula. If we then do:

0 = (W²)+3W - 40 we now have our necessary a, b, and c

Where a = 1, b = 3, c = -40

(a = 1W²; b = 3W, c = -40)

The quadratic formula is the following, and we are going to set it up to find the Width as that is the terms our founded formula is in. 

W = [-b +/- sqrt((b²) - 4ac))]/2a

Now plug in the numbers, first we’ll do the positive (+) in the quadratic formula

[-3 + sqrt[((3²)-4(1)(-40))]/2(1)

[-3 + sqrt[(9+160)]/2

[-3 + sqrt(169)]

[-3 + 13]/2

[10]/2

=5

W = 5

Now that we know W we can find L

L = W+3

L = 8

To check..

Area = L x W

Area = 5 * 8

Area = 40 

We also need to do the subtraction in the quadratic formula, all math is the sqrt is the same. 

[-3 - sqrt[((3²)-4(1)(-40))]/2(1)

[-3 - sqrt[(9+160)]/2

[-3 - sqrt(169)]

[-3 - 13]/2

[-16]/2

=-8 and negative widths/lengths DNE

Hope this helps!

Best,

Andrea A