The figure above shows the dimensions of a rectangular board that is t

Question

https://gmatclub.com/forum/download/file.php?id=50466 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) A. 5 ft 6 in B. 5 ft 3\sqrt{2} in C. 5 ft 3 in D. 5 ft E. 4 ft 9 in PS15302.01 ps4.JPG 2019-09-21_1803.png

KarishmaB · Accepted Answer

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. Ques.jpg 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.

topcisco · Answer

AB+BC=120 
AB=BC+6

then 
AB=63 inches

ans is C.

tkarthi4u · Answer

Same method

We can write the length of the rectangle as 2x + 2y = 240

x + y 120 -----------1

given X = 45 degrees, we draw a line perpendicular to line AB and form a right triangle with X as one of the internal angles.

From that triangle we can write tan45 = 6/y-x

y - x = 6 ---------2

Sove both we get y = 63 inch

Done.

powerka · Answer

Would anybody know if this is a GMAT question?

I had never seen before a GMAT question requiring knowledge of trigonometry.

Thanks

Jivana · Answer

qB = 10 ft.
Since x = 45, angle Ast=45, since traingle Ast is a isoseles triangle.

Therefore, At = st = 6 inches = .5 ft

Now, qA + tB = 10 - .5 
We know that qa = tB since both the pieces must be identicial and rs = At & pz = qB

Therefore, qA + tB = 10 - .5 
or, 2tB = 10 - .5 = 9.5
or, tB = 4.75
AB = tB + At = 4.75 + .5 = 5.25 = 5 ft 3 in.

Hence, C

Sarang · Answer

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.

Battleready79x · Answer

Simply loved your explanation, short and crisp. No unnecessary formulae, simple common sense. I envy you, for the thought didn't strike me. I solved it but in a lengthy way. Thank you. It's a moment of qualia for me.

reynaldreni · Answer

There are 4 identical parallelograms. 
From the figure, we see on each side of the rectangle we have 2 Long sides of the parallelogram and 2 small sides of the parallelogram.
From the figure, we can write,
2L+2S = 20 or L+S = 10
AB is a long side, hence we need to deduce the value of 'L'
S=10-L

From ABDE we can write L = S+AF
AFD is 45-45-90 triangle and AF = 1/2 ft
L = S+1/2
L = 10-L+(1/2)
2L = 21/2
L = 21/4
L = 5.25 ft
L = 5ft + 0.25ft = 5ft 3in

w4rlk · Answer

This question is from OG - Advanced Questions.  Bunuel  or any of the moderators, please tag it so it can be identified for other users.

PS15302.01

Bunuel · Answer

_____________________
Added the tag. Thank you.

ThatDudeKnows · Answer

Here's an approach that hasn't yet been posted. First, the right side of the diagram is irrelevant distractor information. Let's get rid of it. Once we've done that, let's cut the thing in half horizontally. The red line is half way from the left side of the figure to the right side, and the height of the red line is 3 inches. That means that A is three inches to the left of the red line, so three inches from the center. The center is at 5 feet, so A is 5 feet 3 inches from B.

Answer choice C.

Thonereturns · Answer

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.

raahulthakur · Answer

The area of all the pieces is same so, 4*A(Pieces) = 240*6 (Area of Rect) Let's draw a perpendicular to make a triangle APQ, and Q lies between A and B and P on the other side of A, making the line AP as one side of the triangle. Now, area of one piece =1/2 * base * height (Area of triangle APQ) + 6*QB (Area of Quad PQRB) => Area of APQ = 36 Therefore, 4(1/2*36 + 6QB) = 240*6 => 18 + 6QB = 60*6 => 6QB = 60*6-18 => QB = 60*-3 => QB = 57 AB = AQ+QB = 6+57 = 63

pramodmundhra15 · Answer

Can't we use the formula of a trapezoid and solve this question ?
which is 1/2*sum of parallel sides*height.

egmat · Answer

Hello  pramodmundhra15

Yes, we absolutely can use the formula of trapezoid to solve the problem. But we will have to use an inference by drawing up a triangle. Let me illustrate to you what I mean.

SOLVING THE PROBLEM USING TRAPEZOID FORMULA

https://i.imgur.com/x6tJJUI.png

The figure in the question is divided into 4 identical trapezoids with equal area.

The total area of the rectangle = Length * Width 
  = (20 * 12) * 6 = 240 * 6 inch2     
 So, sum of areas of all 4 trapezoids = 240 * 6 inch2  
 Hence,  area of each trapezoid = (240 * 6)/4 = 360    -----(1)

Now, let’s try to get the area of one trapezoid using a different way – using the formula for area of trapezoid. Consider the trapezoid with one side AB: (We have named the side parallel to AB as DE.)
 https://i.imgur.com/2k9YiSt.png

Area of trapezoid ABED = ½ * (Sum of parallel sides) * (Height between parallel sides)
  = ½ * (AB + DE) * BE 
 = ½ * (AB + DE) * 6  
 =  3 * (AB + DE)  ------------- (2)

Combining (1) and (2), we get: 3 * (AB + DE) = 360, or  (AB + DE) = 120  ----- (3)

Now, recall that the question wants us to find AB, but we cannot get that from equation (3) alone, since there are 2 unknowns AB and DE. Hence, we must find another equation relating AB and DE. See that we haven’t yet used the 45 degree angles given – it’s time!

Let’s again enter trapezoid ABED. Drop a perpendicular from D on line AB to create triangle ADF .
 https://i.imgur.com/ndWuCae.png

In triangle AFD:
  Angle A = x = 45 degrees and angle AFD = 90 degrees. Hence, angle FDA is also 45 degrees, making triangle AFD a 45-45-90 triangle. 
 Thus, AF = FD = 6.   --- (4)   
 Finally, observe the above figure to infer that AB = AF + FB and FB = DE. 
  Thus, AB = AF + DE
  AB = DE + 6   
 Or  DE = AB – 6  ------ (5)

From (3) and (5), (AB + AB – 6) = 120
  (2AB – 6) = 120 
 2AB = 120 + 6 
 Therefore, AB = 126/2 =  63 inch

Converting it into feet we get, AB = 63/12 =  5 feet 3 inches.

So, you see that we could use the formula of trapezoid, but to draw the relationship between AB and DE, it was helpful to draw the triangle.

Hope it helps!

Best Regards,
Ashish Arora
Quant Expert, e-GMAT

aanchalgupta25 · Answer

My approach: Drawing perpendicular from D on AG ( lets name the point as G) gives AG = 6 inches. Let GB= x inches. We now apply formula for area of a trapezoid where 1/2 * ( sum of parallel sides = 6+x+x=6+2x) and distance between them= 6 inches. This is also equal to 1/4th of area of rectangle = 240 *6 inches, since the rectangle is made of 4 equal trapezoids. So our equation becomes 1/2 * (6+2x) * 6 = 1/4 * 240 * 6.
Ans >> x= 63 inches or 5ft 3 inches.

Experts, can someone please review this solution and provide comments if this is not the correct approach? Thanks in advance.

joe123x · Answer

how did you get to 63? 
120-6 = 114/2 = 57?

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