Mid-segments

Geometry Level 2

In a scalene triangle Lorenc has drawn it's three mid-segments.Clearly,these mid-segments form a triangle.If the area of the larger triangle is $S$ and the area of this little triangle is $S_1$ ,what is $\frac{S}{S_1}$ ?

The answer is 4.

2 solutions

Ritam Baidya
Nov 28, 2014

well i see that we are given the three mid-points on the respective sides of the triangle....thus we obtain we small half overlapping parallelograms ....and we know that the diagonal divides it into 2 congruent triangle...so we get 4 congruent triangles of equal area HENCE area of any triangle will be ONE-FOURTH to that of the scalene triangle..so ans is 4:1

Yash Singhal
Jun 5, 2014

Let the sides of the bigger triangle be a,b and c.So, the sides of the smaller triangle will be a/2,b/2 and c/2(using midpoint theorem). Now use heron's formula for finding the area of each triangle. Its too easy!!!

Mid-segments

The answer is 4.

2 solutions

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