Help! Math word problem

[Rachiesweet14]

An architect created a plan for a four story building with a central courtyard.
The building measures 96 feet on each side. The courtyard measure 40 feet on a side. His clients asked him to work out an alternative design with the same volume but without the courtyard. Find the side length of such a building if it is designed as a four-story square prism.

Any help would be wonderful thanks. The picture is sideways sorry.

 

[tkhunny]

Not quite sure what the question is.

Ponder on this:

\(\displaystyle 96^{3} - 40\cdot 40\cdot 96 = A^{3}\)

"A" might be the side of your courtyard-less cube.

 

[soroban]

Hello, Rachiesweet14!

An architect created a plan for a four-story building with a central courtyard.
The bulding measures 96 feet on a side; the courtyard measures 40 feet on a side.
is clients asked him to work out an alternative design with the same volume
but without the courtyard.

Find the side length of such a building if designed as a four-story square prism.


View attachment 1917

I assume that the modified building has the same four-story height.

The area of the base is: .\(\displaystyle 90^2 - 40^2 \,=\,7616\text{ ft}^2.\)

Hence, the solid square base has side: .\(\displaystyle \sqrt{7616} \:=\:8\sqrt{119} \:\approx\:87.27\text{ ft.}\)

 

[Rachiesweet14]

Hello, Rachiesweet14!


I assume that the modified building has the same four-story height.

The area of the base is: .\(\displaystyle 90^2 - 40^2 \,=\,7616\text{ ft}^2.\)

Hence, the solid square base has side: .\(\displaystyle \sqrt{7616} \:=\:8\sqrt{119} \:\approx\:87.27\text{ ft.}\)

You said 90, did you mean 96?