Since the height and base are given those are the lengths of the 2 side lengths so to find the perimeter we do 4.8+4.8+8.4+8.4
the answer should be 26.4!
The top of the flag pole touched the ground 12 feet from the base.
Since it cracked 9 feet from the base, 9 is the vertical leg of the right triangle formed. The rest of the flagpole, 24-9=15, is the hypotenuse, as it is slanted down to the ground. The missing side is the horizontal leg, which we will call b:
9²+b²=15²
81+b²=225
Subtract 81 from both sides:
81+b²-81=225-81
b²=144
Take the square root of both sides:
√b²=√144
b=12
A = 2 a² + 2 a b
2 a² + 2 a b = 147/2
a² + a b = 36.75
a b = 36.75 - a²
b = ( 36.75 - a² ) / a
V = a² * b
V = a² * ( 36.75 - a² ) / a
V = 36.75 a - a³ ( maximum of the volume is when V` = 0 )
V` = 36.75 - 3 a²
36.75 - 3 a² = 0
3 a² = 36.75
a² = 36.75 : 3
a² = 12.25
a =√12.25
a = 3.5 ft
b = 24.5 / 3.5 = 7 ft.
Answer: The depth of the shelter for which the space inside is maximized is 3.5 ft.
