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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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Joined: 02 Sep 2009
Posts: 44347
The length of side PR of ∆ PQR is 3 times the length of side AC of ∆ A [#permalink]

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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

[Reveal] Spoiler:
Attachment:

2017-08-08_2134.png [ 15.85 KiB | Viewed 517 times ]
[Reveal] Spoiler: OA

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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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08 Aug 2017, 11:46

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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08 Aug 2017, 19:10
Bunuel wrote:

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

[Reveal] Spoiler:
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

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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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