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16 Jun 2022, 23:30
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If parallelogram PQRS is inscribed in rectangle ORQT, as shown above, and the rectangle has a perimeter of 26, what is the perimeter of the parallelogram?
(1) Area of parallelogram PQRS is 24.
(2) Area of the triangle RST is 6.
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18 Jun 2022, 12:13
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Bunuel
If parallelogram PQRS is inscribed in rectangle ORQT, as shown above, and the rectangle has a perimeter of 26, what is the perimeter of the parallelogram?
(1) Area of parallelogram PQRS is 24.
(2) Area of the triangle RST is 6.
Breaking Down the Info:
Note the proper naming of the shapes should be parallelogram PQSR and rectangle ORTQ according to the graph. We know OR + RT = 13, we want to know PR + RS.
Statement 1 Alone:
This gives us RT * PR = 24. We currently have 2 equations and 3 variables so nothing is solvable. Insufficient.
Statement 2 Alone:
Same as above, insufficient.
Both Statements Combined:
Now we know the area of the rectangle is 24 + 6 + 6 = 36. The perimeter is also 26, hence L*W = 36 and L + W = 13. We don't have to solve this, we just need to know there is only one viable solution for this set of equations in a geometry question. Then since we have L and W figured out, we can find the rest of the lengths using the areas from earlier. Sufficient.
Answer: C
25 Jun 2022, 10:25
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JerryAtDreamScore
Bunuel
If parallelogram PQRS is inscribed in rectangle ORQT, as shown above, and the rectangle has a perimeter of 26, what is the perimeter of the parallelogram?
(1) Area of parallelogram PQRS is 24.
(2) Area of the triangle RST is 6.
Breaking Down the Info:
Note the proper naming of the shapes should be parallelogram PQSR and rectangle ORTQ according to the graph. We know OR + RT = 13, we want to know PR + RS.
Statement 1 Alone:
This gives us RT * PR = 24. We currently have 2 equations and 3 variables so nothing is solvable. Insufficient.
Statement 2 Alone:
Same as above, insufficient.
Both Statements Combined:
Now we know the area of the rectangle is 24 + 6 + 6 = 36. The perimeter is also 26, hence L*W = 36 and L + W = 13. We don't have to solve this, we just need to know there is only one viable solution for this set of equations in a geometry question. Then since we have L and W figured out, we can find the rest of the lengths using the areas from earlier. Sufficient.
Answer: C
Solving L*W=36 and L+W=13, we get two pairs of solutions :
(L,W) = (9,4)
(L,W) = (4,9)
Whether it will not impact the outcome of the question ?
