SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given sides of the first rectangular prism
[tex]h=6m,l=5m,w=4m[/tex]STEP 2: Write the formula for calculating the surface area of the first rectangular prism
[tex]\text{Surface area=}2\left(lw+lh+hw\right)[/tex]STEP 3: Caclulate the surface area of the first rectangular prism
[tex]\begin{gathered} Surface\text{ area=}2\left\lbrack\left(5\times4\right)\right?+\left(5\times6\right)+\left(6\times4\right) \\ surface\text{ area=2\lparen20+30+24\rparen=2\lparen74\rparen=148} \\ \\ \therefore surface\text{ area}=148m^2 \end{gathered}[/tex]STEP 4: Give the dimensions of a second recatngular prism that will have same surface area
We assume three dimensions that will give same 148 squared meter for the second rectangular prism
[tex]\begin{gathered} Suppose;l=11,w=4,S.A=148m^2 \\ \\ we\text{ solve for h} \\ Using\text{ the formula in step 2} \\ S.A=2\left(lh+lw+hw\right) \\ 148=2\left\lbrack\left(11h)+\left(11\times4\right)+\left(4h\right)\right)\right? \\ 148=2\left(15h+44\right) \\ Divide\text{ both sides by 2} \\ \frac{148}{2}=15h+44 \\ 74=15h+44 \\ Subtract\text{ 44 from both sides} \\ 74-44=15h+44-44 \\ 30=15h \\ Divide\text{ both sides by 15} \\ \frac{30}{15}=\frac{15h}{15} \\ 2=h \\ h=2 \end{gathered}[/tex]Hence, the dimensions of the second rectangular prism that will have the same surface area are:
length = 11m
width = 4m
height = 2m
