Question

The value of the surface area of a rectangular prism is equal to the value of the volume of the rectangular prism write and solve an equation to find the value of x

Answer 1

see the attached figure to better understand the problem

Step 1

Find the volume of the rectangular prism

The volume of a rectangular prism is equal to

`V=x*6*6\\V=36*x\ units^(3)`

Step 2

Find the surface area of the rectangular prism

we know that

the surface area is equal to

SA=2*area of the base+perimeter of base*height

area of the base=6*x units^{2}

perimeter of base=2*(6+x)=(12+2*x) units

height=6 units

substitute

SA=2*(6*x)+(12+2*x)*6

SA=12*x+72+12*x-------> SA=(24*x+72) units^{2}

Step 3

equate the value of the volume with the value of the surface area

36*x=(24*x+72)

36*x-24*x=72

12*x=72

x=72/12-------> x=6 units

therefore

the answer is

the value of x is 6 units