Answer:
[tex]x = 2[/tex] ; [tex]y = 4[/tex] and [tex]z = 7[/tex]
Step-by-step explanation:
Given
Let the sides of the cuboid be: x, y and z
[tex]Surface\ Area = 100[/tex]
Required
Find x, y and z
The surface area is calculated as:
[tex]Surface\ Area = 2*(xy + xz + yz)[/tex]
Substitute [tex]Surface\ Area = 100[/tex]
[tex]100 = 2*(xy + xz + yz)[/tex]
Divide both sides by 2
[tex]50 = xy + xz + yz[/tex]
Rewrite as:
[tex]xy + xz + yz =50[/tex]
Now, we use trial by error method to determine the values of x, y and z.
Let [tex]x = 2[/tex] and [tex]y = 4[/tex]
Solve for z:
[tex]2 * 4 + 2*z + 4*z =50[/tex]
[tex]8 + 2z + 4z =50[/tex]
Collect like terms
[tex]2z + 4z =50-8[/tex]
[tex]6z =42[/tex]
Divide both sides by 6
[tex]z = \frac{42}{6}[/tex]
[tex]z = 7[/tex]
So, we have:
[tex]x = 2[/tex] ; [tex]y = 4[/tex] and [tex]z = 7[/tex]
The above values are all integers;
Hence, it is possible to determine a cuboid with the stated requirement
