The length of a rectangular box is 10cm, and the width is four centimeters more than the height. The volume is 450cm^3. Find the width and the height.

Question

Can you please provide me with the steps to how you got the answer as well as the final answer? Thank you so much!

Answer 1

V = lwh

450 = 10(h + 4)h

450 = 10h² + 40h

h² + 4h - 45 = 0 (divided by 10 to make it easier to deal with)

We need two factors if 1(-45) = -45 whose sum is 4.

10 and -4? Nooooo.

-9 and 5? Not quite.

9 and -5? Ding ding ding!

h² + 9h - 5h - 45 = 0

What's common between h² and 9h? h.

h² + 9h = h(h + 9)

What's common between -5h and -45? -5

-5h - 45 = -5(h + 9)

Notice both have h + 9. We combine the common factors into their own set of parentheses.

h² + 9h - 5h - 45 = (h+ 9)(h - 5)

Oh, shoot, I forgot it equals 0.

(h + 9)(h - 5) = 0

Since we have two factors, h + 9 and h - 5, whose product is 0, one has to equal 0.

h + 9 = 0

h = -9

Well, we don't measure using negative numbers, so this is out!

h - 5 = 0

h = 5

There we go.

Since w = h + 4...

w = 5 + 4

w = 9

So, we have a height of 5 cm and a width of 9 cm.

Boom.