Finding two sides of a cuboid while knowing the volumeThe volume of a cuboid is 150 m 3 , one side is 2,5m, one side is completely unknown (x) and the other one is 4 meters longer x + 4. guessed the sides one being 6 and the other 10 but I need to figure it out with a formula.

Question

Finding two sides of a cuboid while knowing the volumeThe volume of a cuboid is   150              m        3  , one side is 2,5m, one side is completely unknown (x) and the other one is 4 meters longer   x  +  4.  guessed the sides one being 6 and the other 10 but I need to figure it out with a formula.

reinmelk3iu · Accepted Answer

Step 1The formula for volume is   V  =  l  w  h where l is the length, w is the width, and h is the height.You are given:  V  =  150  w  =  2.5  l  =  x  h  =  x  +  4.Plugging the values into the formula for volume of a cuboid, you get  150  =  2.5  x  (  x  +  4  )  300  =  5      x    2    +  20  x  60  =      x    2    +  4  x      x    2    +  4  x  −  60  =  0.Step 2Now, this last equation is a quadratic in x, which can be solved by factoring:  (  x  +  10  )  (  x  −  6  )  =  0.  x  +  10  =  0   or   x  −  6  =  0  x  =  −  10   or   x  =  6.The root   x  =  −  10 is extraneous. Therefore,   x  =  6 and   x  +  4  =  10.

szklanovqq · Accepted Answer

Explanation:If you use the volume formula for this cuboid you get   150  =  2.5  x  (  x  +  4  ), and you can divide by 2.5 to get   x  (  x  +  4  )  =  60, which rearranges to a quadratic equation.

The volume of a cuboid is 150m^3, one side is 2,5m, one side is completely unknown (x) and the other one is 4 meters longer (x+4). I guessed the sides one being 6 and the other 10 but I need to figure it out with a formula.

Answered question

Answer & Explanation

New Questions in High school geometry