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The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ A

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The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ A [#permalink]

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New post 08 Aug 2017, 10:36
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The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ ABC. If the length of QS is twice the length of BD, the area of ∆ PQR is how many times the area of ∆ ABC?

(A) 2/3
(B) 3/2
(C) 3
(D) 5
(E) 6

Attachment:
2017-08-08_2134.png
2017-08-08_2134.png [ 15.85 KiB | Viewed 590 times ]

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Re: The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ A [#permalink]

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New post 08 Aug 2017, 11:46
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Given data: PR = 3*AC and QS = 2*BD

Since the area of the ∆ ABC is \(\frac{1}{2}*AC*BD = x\)
Similarly the area of the ∆ PQR = \(\frac{1}{2}*PR*QS = \frac{1}{2}*3*AC*2*BD = 6*\frac{1}{2}*PR*QS = 6x\)

Therefore, Area of ∆ PQR = 6(Area of ∆ ABC) (Option E)
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The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ A [#permalink]

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New post 08 Aug 2017, 19:10
Bunuel wrote:
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The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ ABC. If the length of QS is twice the length of BD, the area of ∆ PQR is how many times the area of ∆ ABC?

(A) 2/3
(B) 3/2
(C) 3
(D) 5
(E) 6

Attachment:
2017-08-08_2134.png

Let AC = x
Let BD = y
Then

PR = 3x
QS = 2y

Area of ∆ ABC = \(\frac{x*y}{2}\)

Area of ∆ PQR = \(\frac{3x*2y}{2}\) = \(\frac{6xy}{2}\)

Factor out the denominator in both areas.

Area of ∆ PQR/area of ∆ ABC =\(\frac{6xy}{xy}\) = 6

Answer E
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The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ A   [#permalink] 08 Aug 2017, 19:10
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