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The figure above shows the dimensions of a rectangular board [#permalink]

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26 Jul 2003, 12:44

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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

Does ETS want me to draw up these right triangles inside the picture?

_________________

Ride em cowboy

Last edited by Curly05 on 30 Jul 2003, 17:31, edited 1 time in total.

Let BC = x and AB = y. Since we need to divide it into 4 identical parts, it can be done so only if PA = x and CQ = y

(P QRS are the corners of the original diagram and P being on the left of A and Q is on the right of C )

=> 2(x+y) = 20 x 12 = 240inches.

x+y = 120 inches. (1)

Now draw a perpendicular from the top of the line drwan at L45 from C .
This will give us y - x = 6 (2)
Solving (1) and (2) , we get y =ve us 6 = y - x
=> 6 = CQ - NQ = y - x (2)
63 inches.

Sorry , I could not put it in a good diagram !!
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by visual inspection and by symmtry it is for sure that AB is greater than 5 feet .... and by calcualting u get 5 feet 3 inches for the lenght of AB !!!@@##$$
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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) First of all, is a rectangle broken up into three right triangles?

Do this systematically. The problem says that the plank is cut into four identical pieces. Right away you should realize that the area of each piece is 1/4 of that of the plank.

Well, the plank is 20 x 1/2 or 10 square feet. Hence the area of each trapezoid is 5 x 1/2 = 2.5 square feet.

Well, let the short base of the trapezoid = x. Since the angle = 45 deg, the long side must be x + the height of the trap = x + 1/2.

Well the area of a trapezoid is the average of the bases * the height = 1/2*(x + x + 1/2)*1/2 = 2.5. Solving for x we get x = 4.75. Since we want the length of the longer side, we get 4.75 + .5 = 5.25 feet = 5'3".
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

I think you mean 1/4- four equal trapez. * 10 feet-area= 2.5 feet,

Why 5 *1/2= Explain.

Right on, how did you assume they are trapezoid's. ETS way of don't assume anything is misleading. How do you attack that?

Good job Akami, you are gift to the Gmatclub along with others.

I know they are trapezoids because you cut into a rectangle and a rectangle has parallel sides.

Area of rectangle was 20 * 1/2. Area of trapezoid is 1/4 of that, so 5 * 1/2.
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

drop a perpendicular from the top of the first cut from the left. This creates a 45, 45, 90 triangle, which tells you that the base of the triangle is 6 inches. Half of the plank is 5 feet and half of the triangle is 3 inches.