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The area of the parallelogram in the figure above
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08 Jun 2021, 09:00
08 Jun 2021, 09:00
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The area of the parallelogram in the figure above is 40. If QR = 10 and ST = 7, then the perimeter of the parallelogram is
(A) 30
(B) 36
(C) 40
(D) 45
(E) 50
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Re: The area of the parallelogram in the figure above
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08 Jun 2021, 09:18
08 Jun 2021, 09:18
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Carcass wrote:
The area of the parallelogram in the figure above is 40. If QR = 10 and ST = 7, then the perimeter of the parallelogram is
(A) 30
(B) 36
(C) 40
(D) 45
(E) 50
Since PQRS is a parallelogram, we know that QR = PS, so side PS also as length 10
Next, the area of a parallelogram = (base)(height)
The base has length 10 and we're told the area = 40
So, we get: (10)(height) = 40, which means the height = 4
We're also told that ST = 7
Since PS has length 10, we can conclude that PT has length 3
Now focus on the RIGHT TRIANGLE ∆PQT
When we apply the Pythagorean Theorem, we see that side PQ (the hypotenuse of ∆PQT) has length 5, which means the side opposite PQ (side RS) also has length 5
So, the perimeter of the parallelogram 10 + 5 + 10 + 5 = 30
Answer: A
gmatclubot
Re: The area of the parallelogram in the figure above [#permalink]
08 Jun 2021, 09:18
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