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In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a

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by BTGmoderatorDC » Fri Jul 24, 2020 6:06 pm

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Answers

A

B

C

D

E

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QR DS 91.jpg
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.


OA D

Source: Official Guide
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Re: In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a

by dashingnightmare » Fri Jul 24, 2020 9:53 pm
A.
Since both ladders are of same length, we need any 1 length
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Re: In the figure above, segments RS and TU represent two positions of the same ladder leaning against the side SV of a

by hahahehe » Sat Jul 25, 2020 5:00 am
I won't take out the final numbers, but rather tell how you should do in exam.
First rule, in a triangle, if you know the length of a side and both of the angles associated with that side, you will be able to construct the triangle uniquely. Try it out, fix the base, and decide on two angles that the other side will form with this base. The two lines will eventually intersect, giving you unique triangle.

Statement 1: TU = 10 meters. In triangle TUV, we now know TU (10m), we know angle T (45), and we know angle U (45, sum of angles in triangle is 180).. So we can calculate all sides' lengths.
In RSV also, we know RS = TU (since same ladder: mentioned in question itself). We know angle R (60) and we know angle S(30). So we can calculate all length of all sides for it as well. Since everything can be calculated, we can calculate the difference TR.

Statement 2: RV = 5 meters. We know angle R (60) and angle V(90). So we can know length of RS and SV.
Now that RS can be calculated, we know RS = TU. So in triangle TUV, we again know TU, angle T, and angle U, and hence can calculate everything else.

So answer is D.
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