Answer:
height = length = width = [tex]\sqrt{\frac{74}{3}}[/tex]
Step-by-step explanation:
You first calculate the surface area of the given prism, by using the following formula:
[tex]A=2(wh+lw+lh)[/tex] (1)
where
w: width = 4
h: height = 6
l: length = 5
[tex]A=2(4*6+5*4+5*6)=148[/tex] (2)
The best way to find the dimension of another rectangular prism with the same surface area of (2), is to assume that w=h=l=a. Thus, you have in the equation (1):
[tex]A=2(3a^2)=6a^2[/tex]
You replace the value of A and solve for a:
[tex]148=6a^2\\\\a=\sqrt{\frac{148}{6}}=\sqrt{\frac{74}{3}}[/tex]
Then, the dimensions of the new prism are:
height = length = width = [tex]\sqrt{\frac{74}{3}}[/tex]
