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WARRIOR [948]
3 years ago
6

Mr.Manciel is planning an event at a local hotel. The hotel owner told him that the dance floor in the ballroom is about 1,500 s

quare feet. When Mr. Manciel measured, he found that the dimensions of the dance floor are 25 feet by 44 feet. Was the hotel owner ‘s estimate reasonable? Why or why not?
Mathematics
1 answer:
murzikaleks [220]3 years ago
8 0
Yes it was reasonable. I say it is resonable because if you multiply 44 times 25 it is 1,100 so the estimate was close enough
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ONLY SERIOUS ANSWERS!!!! 25 POINTS
AveGali [126]

Answer:

FD≈25.94.. rounded = 26

Step-by-step explanation:

FD²=12²+(4x+11)²

FD²=144+16x²+88x+121

FD²=265+16x²+88x

also

FD²=12²+(13x-16)²

FD²=144+169x²-416x+256

FD²=400+169x²-416x

thus

265+16x²+88x = 400+169x²-416x

16x²-169x²+88x+416x+265-400 = 0

-153x²+504x-135 = 0

we will solve this quadratic equation by suing the quadratic formula to find x

x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)

x=(-504±\sqrt{504^{2}-4(-153)(-135) })/2(-153)

x=(-504±\sqrt{254016-82620 })/-306

x=(-504±\sqrt{171396})/-306

x=(-504±414)/-306

x=(-504+414)/-306 and x=(-504-414)/-306

x=-90/-306 and x=-918/-306

x= 5/17 , 3

substituting x by the roots we found

check for 5/17:

4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..

13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..

check for 3:

4x+11 = 4×3+11 = 12+11 = 23

13x-16 = 13×3-16 = 23

thus 3 is the right root

therfore

ED=23 and CD=23

FD²=FE²+ED² or FD²=FC²+CD²

FD²=12²+23²

FD²=144+529

FD²=673

FD=√673

FD≈25.94.. rounded = 26

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