When the height of a rectangular prism was halved, the volume was 168 cubic cm. if the original prism had a length, width, and h

Question

2 years ago

5

When the height of a rectangular prism was halved, the volume was 168 cubic cm. if the original prism had a length, width, and h

eight of consecutive integers, increasing in that order,
(a) write and equation to solve for the length, x, of the original figure,
(b) solve length, x,
(c) show that the equation is unique
show all work.

Mathematics

1 answer:

kondaur [170] · Answer 1 · 2023-03-22T14:19:54+03:00

a) The equation is therefore; x³ + 3x² + 2x = 336

b) Solving for the length, we get the length to be; x = 6.

c) All workings are as shown below;

According to the question;

When the height of a rectangular prism was halved, the volume was 168 cubic cm.

In essence, the volume of the original prism is;

Volume = 168 × 2.

Volume = 336cm³

Since, the original prism had a length, width, and height of consecutive integers, increasing in that order.

Therefore, length = x

width = (x +1)

height = (x +2)

Volume = x (x+1) (x+2) = 336

a) The equation is therefore;

<em>x³ + 3x² + 2x = 336</em>

b) Solving for the length, x is as follows;

(x-6) (x² + 9x + 56) = 0

By testing values and checking;

Upon solving the polynomial, x = 6.

c) All workings are as shown above.