Answer:24 and 32 ft or 32 and 24 ftStep-by-step explanation:Perimeter of rectangle(p)=2(l+b)or, 112/2=l+bTherefore, l+b=56Now,diagonal(d)=40By pythogoras theorem,h^2=p^2+b^2 (d=h here)40^2=l^2+b^2Now,Square l+b=56(l+b)^2=56^2l^2+2lb+b^2=31362lb=3136-1600lb=1536/2Therefore, lb=768 b=768/lNow, Perimeter of rectangle(p)=2(l+b)l+b=56l+768/l=56l^2+768=56ll^2+768-56l=0 Factoring,(l - 32) (l - 24) = 0Either l= 32 or l = 24When l=32,l+b=5632+b=56b=24When l=24l+b=5624+b=56b=32So the dimensions of the dance floor are 24 and 32 ft or 32 and 24 ft.