The volume of the block is the product of its length, width, and height.
Let's use the information given to write and simplify an expression for the volume of the block.
According to the Rational Root Theorem, we can find the rational roots of this equation as quotients of factors of the constant term -945, and factors of the leading coefficient 144.
Let's focus on the possible integer solutions, the factors of -945.
Let's try the factors from smallest to largest until we find a solution or get a volume above 945.
Height (x)
Length (12x-15)
Width (12x-21)
Volume
1
12( 1)-15=-3
12( 1)-21=-9
Not meaningful.
3
12( 3)-15= 21
12( 3)-21= 15
3* 21* 15=945 âś“
Note that height, length, and width are all increasing functions of x, which means that the volume is also an increasing function of x.
This means that the only solution to the problem is the one we found above.
2
&Length:&& 21m
&Width:&& 15m
&Height:&& 3m
