Quadrilateral parking lot
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Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. What is the area of the parking lot?
1) RU = 80 meters
2) TU = 20(root10) meters
d
Experts-
I can see the hidden right triangle in the picture, but how much of the calculation do I really need to complete to know when each statement is sufficient?
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This is a DS question. In most DS questions, you need not do the complete calculation to decide whether the statement (s) is sufficient to answer the question.JJMforthegold wrote:
Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. What is the area of the parking lot?
1) RU = 80 meters
2) TU = 20(root10) meters
d
Experts-
I can see the hidden right triangle in the picture, but how much of the calculation do I really need to complete to know when each statement is sufficient?
In this question also, you need not do the calculation. A mere analysis would suffice.
We have to find out the area of RSTU.
Since ST and RU are parallel to each other, the area of trapezium would be:
(Sum of parallel sides)*(Height of the trapezium)/2
Area of RSTU = (ST + RU)*SW/2 = 30(45 + RU)
Question rephrased: What is the length of RU?
Statement 1: RU = 80 meters
We have the value of RU. Sufficient.
No need to calculate the area.
Statement 2: TU = 20√10 meters.
Let's draw a perpendicular from T on RU. Say it meets RU at U'. Thus, triangle TU'U is a rightangled triangle, where TU' = SW = 60.
So, in for rightangled triangle TU'U, we have hypotenuse TU = 20√10, TU' = 60.
By applying Pythagoras theorem, we can get the value of U'U.
UU'^2 = TU^2 - TU'^2 = (20√10)^2 - 60^2 = A unique value (let's not calculate).
We still did not get the value of RU.
RU = RW + WU' + U'U = 15 + ST + A unique value = 15 + 60 + A unique value = A unique value
Thus, we have RU. Sufficient.
The correct answer: D
Hope this helps!
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-Jay
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