Help Needed in Geometry.

[r.jagannathan6]

I stumbled upon 2 different Problems on Geometry for which i need your help.

1) In a triangle ABC, Point D is on side AB and Point E is on the side AC such that BCED is a trapezium. DE:BC = 3:5. Calculate the ratio of the area of Triangle ADE and Trapezium BCED.?

2) D, E and F are the mid points of the sides BC, CA and AB respectively of Triangle ABC. Determine the ratio of the area of triangles ABC and DEF?

Please provide your inputs to solve these 2 problems.

[aditya8062]

1) In a triangle ABC, Point D is on side AB and Point E is on the side AC such that BCED is a trapezium. DE:BC = 3:5. Calculate the ratio of the area of Triangle ADE and Trapezium BCED.?

i am not sure how to draw figures here but i will try to help u with my linguistics as much as possible (though i always feel that geometry without figures makes little sense )
oki so i calculated the answer of this problem as 9/16.firstly u draw a nice diagram of triangle ABC
now coz the problem says that BCED is a trepazium that means that DE is parallel to BC so we have two similar triangle namely ADE and ABC . now similar triangles have areas in ratio of the square of their sides
so we can conclude that area of ADE/area of ABE = 9/25
so to find the area of ADE /area of trepezium BCED = 9/16

[aditya8062]

2) D, E and F are the mid points of the sides BC, CA and AB respectively of Triangle ABC. Determine the ratio of the area of triangles ABC and DEF?

for this one i feel the answer is 1/4
pls confirm the answers

[r.jagannathan6]

Thanks Adithya.

The answer for the first question is 9:16.I could'nt understand the last step in which you arrived at 9:16. I can understand till you arrived at 9:25. Can you please explain on the last step?

For the second step, the answer is 4:5

[aditya8062]

for the second question i mistakenly told u the ratio of DEF to ABC 1:4 when in fact u had asked for the ratio of ABC to DEF .so the answer sud be 4:1 not 1:4
plz confirm the answer .i doubt the answer as what u have mentioned
as for the first one as how i got 9/16 from 9/25 simply subtract 9 from 25 .u see the area of combination of pieces (no matter what ) is always addition of area of individual pieces so if i assume that whole big triangle is of area 25 and that top small similar triangle is area 9 then area of that trapezium is =25-9 =16...right ?

[jlucero]

1. the first question is not a GMAT-like question as evidenced by the usage of the word trapezium. From wikipedia:

In Euclidean geometry, a convex quadrilateral with at least one pair of parallel sides is referred to as a trapezoid in American English and as a trapezium in English outside North America.

A trapezium in American English is a parallelogram with no parallel sides, which would be impossible to solve for.

That said, using the figure below, you should be able to solve for the triangle and the trapezium using these formulas:

ABCDE-2.jpg (41.11 KiB) Viewed 6747 times

Triangle = 1/2bh = 1/2*3*3/5*h
Trapezium = Triangle ABC - Triangle ADE = 1/2*5*h - 1/2*3*3/5*h

Solving for this, you would get a ratio of 9/16

2. Notice how the base and height of the smaller triangle would be half of the base and height of the larger triangle. So you should get a ratio of:

DEF/ABC = (1/2b*1/2h)/(bh) = 1/4

You can also see from the diagram that there are four equal triangles inside the larger triangle.

ABC.jpg (46.37 KiB) Viewed 6650 times

[RonPurewal]

hi,
i'm going to close this thread, because these are clearly not GMAT PREP software questions.

this thread is exclusively for problems from the official software. please do not post problems from any other source here.
thanks.