Nathan B. answered • 04/27/15

Elementary and Algebraic skilled

a) A rectangular prism is just calculating a rectangle in three dimensions, so it's length times width times height, or:

V = lwh

We're told the following:

l = 2 + w

h = 15

So the equation looks like:

V = 15w(2 + w)

or

V = 15w

^{2}+ 30wb) We're given the volume, so our equation now looks like:

2145 = 15w(2 + w)

143 * 15 = 15w(w + 2)

143 = w(w + 2)

143 = w

^{2}+ 2w0 = w

^{2}+ 2w - 143Now we have a quadratic formula. Using what we know, the numbers that multiply together to make 143 have to be only two units apart (so that we can have that 2w in the center), thus very close together. The square root of 143 is almost twelve, so let's try that:

10 * 12 = 120

12* 14 = 168

Close, so let's try another pair around that:

11 * 13 = 143

There we go. Now since we have a

*plus*two, that means the larger number gets the addition sign when we factor out:0 = (w - 11)(w + 13)

So:

0 = w - 11

or:

0 = w + 13

which means w = 11, -13

We can't have a negative length of a side, so the width has to be 11 meters.

l = 11 + 2

l = 13

Now lets check:

2145 m

^{3}= 11m * 13m * 15m2145 m

^{3}= 2145m^{3}Now, when the question asks you to find the

*base*, I assume they mean the flat surface on the ground, so:11m * 13m = 143m

^{2}