Roof Prism
math question applicaitons?

an apartment building is shaped like a box with a square cross section and a triangular prism forming the roof. the total height of the building is 30 feet and the sum of the length and the width of the buildin gis 100ft.

WHAT ARE THE DIMENSIONS OF THE BUILDING WITH MAXIMUM VOLUME AND WHAT IS THE VOLUME

HOW TO DO , IF IMPOSSIBLE, WHAT WOULD BE MAXIMUM VOLUME AND DIMENSIONS

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Maximum size is a square. Since length and width total 100 ft, length equals width so each would be 50 ft.
50 x 50 = 2500 sq.ft, pretty small for an apartment building.
What is the angle of the roof?
A flat roof would be 2500 x 30 = 75000 cu ft.
A roof that touches the ground would be 75000/2 = 37500 cu ft.
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