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The figure above shows the dimensions of a rectangular board [#permalink]
27 Apr 2009, 20:09

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

36% (04:27) correct
64% (02:52) wrong based on 122 sessions

Attachment:

ps4.JPG [ 33.08 KiB | Viewed 5565 times ]

The figure above shows the dimensions of a rectangular board that is to be cut into four identical pieces by making cuts at points A, B, and C, as indicated. If x = 45, what is the length AB ? (1 foot = 12 inches)

Could you explain how did you come up with that equation?

I understood tkarthi4u's explanation. He used the tangent formula: tan(x)= opposite / adjacent -> tan(45) = 6 / (y-x) Given that tan(45)=1, then y-x=6 Together with x+y=120, y=63inches=5ft3in -> answer C

Could you explain how did you come up with that equation?

I understood tkarthi4u's explanation. He used the tangent formula: tan(x)= opposite / adjacent -> tan(45) = 6 / (y-x) Given that tan(45)=1, then y-x=6 Together with x+y=120, y=63inches=5ft3in -> answer C

I don't understand your approach.

Thanks a lot

AB=AD+DB AD is 6 inches since x is 45 degrees. To obtain DB you have to subtract 2*6inces (6 inches because of AD and other 6inches more because CE=AD) to the long side (20 feet) and divide by 4 since there are 4 segments like DB. It´s quiet complicated to explain...

The length of the rectangle is 240 inches. The diagram shows you the isosceles triangle whose side will be 6 inches. From 240, if we remove 2 of these sides of 6 inches each, we will be left with 228 inches.

Attachment:

Ques.jpg [ 8.15 KiB | Viewed 4314 times ]

This 228 inches has to be equally divided into 4 parts as shown by the blue arrows. Why are these parts equal? Because the question says that the four pieces are identical. So the smaller side of each piece has to be equal (Look at the blue line on the top. This should be equal to the blue lines at the bottom).

The length of each of the blue lines will be 228/4 = 57 inches. The length of AB = 57 + 6 inches = 63 inches. _________________

Draw a perpendicular till point P on AB to make it right isosceles triangle- With principle of 45-45-90 you get AP=6. As Karishma told- there are 4 equal area rectangles. thus AB= AP+PB = 57+6 = 63 inches.

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Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

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