A cuboid has sides of length x cm, y cm and 8 cm and volume is 330 cm^3. Given that x + y = 13,

Question

Find the possible values of x and y?

Answer 1

To find the possible values of x and y, we first need to use the formula for the volume of a cuboid:

Volume = length x width x height

Given that the volume is 330 cm^3 and the sides are x cm, y cm, and 8 cm, we can set up the equation:

330 = x * y * 8

Next, we know that x + y = 13, so we can rearrange this equation to solve for y:

y = 13 - x

Now we can substitute this expression for y into the volume equation:

330 = x * (13 - x) * 8
330 = 104x - 8x^2

Rearranging this equation in standard form, we get:

8x^2 - 104x + 330 = 0

Now we can use the quadratic formula to solve for x:

x = [-(-104) ± √((-104)^2 - 4*8*330)] / (2*8)
x = [104 ± √(10816 - 10560)] / 16
x = [104 ± √256] / 16
x = [104 ± 16] / 16

This gives us two possible values for x:

x = 120/16 = 7.5
x = 88/16 = 5.5

Now we can use these values to find the corresponding values for y:

For x = 7.5, y = 13 - 7.5 = 5.5
For x = 5.5, y = 13 - 5.5 = 7.5

Therefore, the possible values for x and y are x = 7.5 cm, y = 5.5 cm or x = 5.5 cm, y = 7.5 cm.