Answer:
24 and 32 ft or 32 and 24 ft
Step-by-step explanation:
Perimeter of rectangle(p)=2(l+b)
or, 112/2=l+b
Therefore, l+b=56
Now,
diagonal(d)=40
By pythogoras theorem,
h^2=p^2+b^2 (d=h here)
40^2=l^2+b^2
Now,
Square l+b=56
(l+b)^2=56^2
l^2+2lb+b^2=3136
2lb=3136-1600
lb=1536/2
Therefore, lb=768
b=768/l
Now,
Perimeter of rectangle(p)=2(l+b)
l+b=56
l+768/l=56
l^2+768=56l
l^2+768-56l=0
Factoring,
(l - 32) (l - 24) = 0
Either l= 32 or l = 24
When l=32,
l+b=56
32+b=56
b=24
When l=24
l+b=56
24+b=56
b=32
So the dimensions of the dance floor are 24 and 32 ft or 32 and 24 ft.
