Ans is C

See the attached pic.

Draw perpendicular from top to the bottom line i.e FD and DE.

Since angle x = 45. So, AD = CE = 6 inches. (you can calculate this from tan 45 = 1)

Now you get 4 equal section HA = DB = BC = EI = y

so 4y+1/2+1/2 = 20. Solve this to get y = 19/4

AB = 19/4 + 1/2 = 21/4 = 5 ft 3 inches ANS

Thanx Kajcha! Thanks a lot. But I have some queries man! Refer it -
In ur post, u mentioned that -

Now you get 4 equal section HA = DB = BC = EI = y

so 4y+1/2+1/2 = 20. Solve this to get y = 19/4

AB = 19/4 + 1/2 = 21/4 = 5 ft 3 inches ANS

U are trying to say that HA+AD + DB + BC + CE + EL = 20
Or, 4y + 6 + 6 = 20 [As AD = 6 and CE = 6]
Therefore, y = 2.

Can u pls explain this point where from get the value of 1/2? Waiting for ur reply!

AD = 6 inches = 1/2 feet. Please note that units of both sides are different. One is 20 FEET and another is 6 INCHES.[/b]

I solved it differently. Consider the portion; with A & B. Clearly B is the median that cut the rectangular board in two halves. if we name the rectangle WXBZ (W being top right corner and then proceed clockwise).

So, ZB = 5 feet.

Now draw the diagonal, WB. This will intersect the line Aa (which makes a angle of 45 degree on ZB), at center which will be the center of the reactangular board also. Let name this point, O.

Now draw a perpendicular from O to ZB, that will intersect the ZB at (say) 'p'. Now Ap = 3 inches (as triangle AOP is isoceles with OP as 3 inches).

As O is the center point, perpendicular drawn from O to ZB will cut it in two halves again, thus; Zp = pB = 5 feet.

And hence, AB = Ap + pB = 5 ft 3 inches.

This solution might be looking lengthy, but it took me 40 sec to solve the question.

Sorry, I'm not providing the diagram (thats y I had to explain all this )

Ohhhhh! Kajcha, thanks a lot for pointing me out my mistake. Yop! Somehow I overlooked that. And niks thanks a lot for ur different appraoch.

Kajcha, or camitava,


Now you get 4 equal section HA = DB = BC = EI = y

How do you presume that the remaining four parts are equal. The rest i get, but this part i just didnt! What am i missing? Thanks!

niks_01.27 wrote:I solved it differently. Consider the portion; with A & B. Clearly B is the median that cut the rectangular board in two halves. if we name the rectangle WXBZ (W being top right corner and then proceed clockwise).

So, ZB = 5 feet.

Hello Niks,

Thanks for that explanation. However, I'm not seeing the rectangle WXBZ. You mentioned that W is the top right corner (do you mean at the other end of the line running from B?).

wongee wrote:Kajcha, or camitava,


Now you get 4 equal section HA = DB = BC = EI = y

How do you presume that the remaining four parts are equal. The rest i get, but this part i just didnt! What am i missing? Thanks!

Wongee, question says that the original pic has 4 IDENTICAL pieces.

In the original pic take the left side of the perpendicular B. Since these 2 pieces are identical smaller side of these 2 will be same. If you draw perpendicular from the F to D you will have a rectangle in which DB is equal to the smaller side of the identical piece.