Answer:
5, 10 and 3
Step-by-step explanation:
We know that that to find the volume of a cuboid you have to multiply the length by width by the height so we can set up an equation to work out the value of x
→ Form equation
( x + 5 ) × ( x - 2 ) × ( x ) = 30x
→ Expand out the brackets
( x² - 2x + 5x - 10 ) × ( x ) = 30x
( x ) × ( x² + 3x - 10 ) = 30x
x³ + 3x² - 10x = 30x
→ Minus 30x from both sides to make an equation
x³ + 3x² - 40x = 0
→ First factor 'x' out of the equation
x ( x² + 3x - 40 ) = 0
→ Now we have to solve the equation
x ( x + 8 ) ( x - 5 ) = 0
( x + 8 ) = 0 so x = -8
( x - 5 ) = 0 so x = 5
We have 2 solutions but since we are finding the volume of a cuboid we don't use the negative value since it isn't logical to have negative number side length's so we discard -8. The true value of x is 5. Now we have to substitute 5 into all of the x length's and the volume to make sure the solution is correct
→ Substitute x = 5 into ( x ), ( x + 5 ), ( x - 2 ) and 30x
→ 5 , 10 , 3 and 150
We know that the side lengths are 5, 10 and 3 and we know that volume is 150 so we multiply the 3 numbers together to make that value of x = 5 is correct so,
5 × 10 × 3 = 50 × 3 = 150
So the value of x = 5 is correct
