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## Need to understand the logic please

This topic has 2 expert replies and 3 member replies
shibsriz@gmail.com Master | Next Rank: 500 Posts
Joined
19 Sep 2012
Posted:
429 messages
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6

#### Need to understand the logic please

Wed Jun 05, 2013 4:03 am
In triangle ABC, point Xis the midpoint of sideAC and
point Yis the midpoint of side BC. If point Ris the
midpoint of line segment XC and if point S is the
midpoint of line segment YC, what is the area of
triangular region RCS1
(1) The area of triangular region ABX is 32.
(2) The length of one of the altitudes of triangle ABC
is 8

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GaneshMalkar Senior | Next Rank: 100 Posts
Joined
31 Jul 2012
Posted:
77 messages
Followed by:
1 members
8
Target GMAT Score:
800
Sun Jun 09, 2013 5:32 am
shibsriz@gmail.com wrote:
Hey Mitch, what I dont understand is that how u got the altitude BZ, i.e ABZ is a rigth angle triangle!

Thanks
Shiba
BZ is the perpendicular drop from the point B to the extended base AC which is the height or altitude of triangle ABC.

_________________
If you cant explain it simply you dont understand it well enough!!!
- Genius

Nina1987 Senior | Next Rank: 100 Posts
Joined
15 Dec 2015
Posted:
79 messages
Followed by:
1 members
GMAT Score:
750
Sat Feb 13, 2016 6:01 am
The question is testing properties of similar triangles here. There 3 ways to tell if the triangles are similar:

1. AAA (angle angle angle)
All three pairs of corresponding angles are the same.
(We actually need two angles really:)

2. SSS in same proportion (side side side)
All three pairs of corresponding sides are in the same proportion

3. SAS (side angle side)
Two pairs of sides in the same proportion and the included angle equal.

It is this 3rd property that is quite handy here. Two triangles ABC and RSC are similar since RC/AC=SC/BC=1/4 and they include the same angle THETA (as shown in the figure)

1) Tells us that Area(ABX) =32. Since height of triangle ABC is same that of triangle ABX and the base is twice, area (ABC) = 32*2= 64. Since ABC and RSC are similar and their sides are in the ration of 1:4 their ares will be in the ration of 1:16. Sufficient to solve.
2) Tells us one of the altitudes is 8. Since it does not tell which one, insufficient!
ttp://postimg.org/image/lc02jbchh/" target="_blank">

GaneshMalkar Senior | Next Rank: 100 Posts
Joined
31 Jul 2012
Posted:
77 messages
Followed by:
1 members
8
Target GMAT Score:
800
Sun Jun 09, 2013 5:32 am
shibsriz@gmail.com wrote:
Hey Mitch, what I dont understand is that how u got the altitude BZ, i.e ABZ is a rigth angle triangle!

Thanks
Shiba
BZ is the perpendicular drop from the point B to the extended base AC which is the height or altitude of triangle ABC.

_________________
If you cant explain it simply you dont understand it well enough!!!
- Genius

Nina1987 Senior | Next Rank: 100 Posts
Joined
15 Dec 2015
Posted:
79 messages
Followed by:
1 members
GMAT Score:
750
Sat Feb 13, 2016 6:01 am
The question is testing properties of similar triangles here. There 3 ways to tell if the triangles are similar:

1. AAA (angle angle angle)
All three pairs of corresponding angles are the same.
(We actually need two angles really:)

2. SSS in same proportion (side side side)
All three pairs of corresponding sides are in the same proportion

3. SAS (side angle side)
Two pairs of sides in the same proportion and the included angle equal.

It is this 3rd property that is quite handy here. Two triangles ABC and RSC are similar since RC/AC=SC/BC=1/4 and they include the same angle THETA (as shown in the figure)

1) Tells us that Area(ABX) =32. Since height of triangle ABC is same that of triangle ABX and the base is twice, area (ABC) = 32*2= 64. Since ABC and RSC are similar and their sides are in the ration of 1:4 their ares will be in the ration of 1:16. Sufficient to solve.
2) Tells us one of the altitudes is 8. Since it does not tell which one, insufficient!
ttp://postimg.org/image/lc02jbchh/" target="_blank">

shibsriz@gmail.com Master | Next Rank: 500 Posts
Joined
19 Sep 2012
Posted:
429 messages
Followed by:
4 members
6
Fri Jun 07, 2013 7:15 am
Hey Mitch, what I dont understand is that how u got the altitude BZ, i.e ABZ is a rigth angle triangle!

Thanks
Shiba

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