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In the figure above, segments RS and TU represent two

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In the figure above, segments RS and TU represent two [#permalink]  22 Feb 2011, 09:36
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50% (01:31) correct 50% (00:25) wrong based on 10 sessions
In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than the length of RV?
(1) The length of TU is 10 meters.
(2) The length of RV is 5 meters.
[Reveal] Spoiler: OA

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Kudos [?]: 1128 [0], given: 376

Re: QR 91 Geomatry [#permalink]  22 Feb 2011, 09:59
$$\triangle{TVU}$$ is a right-angled triangle with angles 45-90-45.
Ratio of its sides
$$Base:Altitude:Hypotenuse::\bar{TV}:\bar{UV}:\bar{TU}::1:1:\sqrt{2}$$

$$\triangle{RVS}$$ is a right-angled triangle with angles 30-90-60.
Ratio of its sides
$$Base:Altitude:Hypotenuse::\bar{RV}:\bar{VS}:\bar{SR}::1:\sqrt{3}:2$$

(1)
TU=RS=10
$$\bar{TV}=\frac{10}{\sqrt{2}}$$
$$\bar{RV}=\frac{10}{2}$$

Find TV-RV
Sufficient.

(2)
RV=10
$$\bar{RS}=5*2=\bar{TU}$$
$$\bar{TV}=\frac{10}{\sqrt{2}}$$
Find TV-RV
Sufficient.

Ans: "D"
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Kudos [?]: 222 [0], given: 123

Re: QR 91 Geomatry [#permalink]  03 Mar 2011, 06:44
Same ladder = same length. TU=RS

In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a wall. The length of TV is how much greater than the length of RV?
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Kudos [?]: 74 [0], given: 3

Re: QR 91 Geomatry [#permalink]  03 Mar 2011, 08:51
You can also use basic trigonometry to get this information. Let's see how:

Statement 1 says TU = 10 metres which would be same as RS as its the same ladder.

Now TV = TU*Cos45 and
and RV = RS*Cos60

So both TV and RV can be calculated by using given information, so sufficient

Statement 2 gives RV = 5, but we know that RV = RS*Cos60 so, RS = TS = RV/Cos60 and hence TV can also be determined. Thus we again know TV and RV, so sufficient.

Re: QR 91 Geomatry   [#permalink] 03 Mar 2011, 08:51
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