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