Answer:
[tex]x=2\sqrt{\frac{14}{3}}\ units[/tex] or [tex]x=\frac{2}{3}\sqrt{42}\ units[/tex]
Step-by-step explanation:
we know that
The surface area of a cube is equal to
[tex]SA=6x^{2}[/tex]
where
x is the length side of a cube
In this problem we have
[tex]SA=112\ cm^{2}[/tex]
substitute in the formula and solve for x
[tex]112=6x^{2}[/tex]
[tex]x^{2}=112/6[/tex]
square root both sides
[tex]x=\sqrt{\frac{112}{6}}\ units=2\sqrt{\frac{14}{3}}\ units=\frac{2}{3}\sqrt{42}\ units[/tex]
The total surface area of this cuboid is 112[tex]\rm cm^2[/tex] then the value of x is 2.65cm and this can be evaluated by using the total surface area of the cuboid formula.
Given :
The total surface area of this cuboid is 112[tex]\rm cm^2[/tex]
The total surface area of the cuboid is given by:
[tex]\rm Suraface\;Area = 6x^2[/tex] ---- (1)
where 'x' is the side length of the cuboid.
Now, put the value of the surface area of the cuboid in equation (1).
[tex]112 = 6x^2[/tex]
[tex]x=\sqrt{\dfrac{112}{6}}[/tex]
[tex]x=\sqrt{\dfrac{56}{3}}[/tex]
x = 2.65cm
Therefore, the total surface area of this cuboid is 112[tex]\rm cm^2[/tex] then the value of x is 2.65 cm.
For more information, refer to the link given below:
https://brainly.com/question/207493
