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In triangle ABC, point X is the midpoint of side AC and point Y is th
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20 Feb 2024, 05:26
20 Feb 2024, 05:26
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60% (02:25) correct
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In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. The point R is the midpoint of line segment XC and point S is the midpoint of line segment YC. If the area of the triangular region ABX is 32, what is the area of the triangular region CRS?
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: In triangle ABC, point X is the midpoint of side AC and point Y is th
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07 Jun 2024, 23:58
07 Jun 2024, 23:58
Expert Reply
A line segment drawn from a vertex to the midpoint of the opposite side divides the triangle into two equal triangles.
Here, in the triangle ABC, a line segment BX drawn from vertex B to the midpoint of AC at X divides triangle ABC into two equal triangles: triangle ABX and triangle CBX.
Thus, Area of triangle CXB = Area ABX = 32.
Again, in the triangle CBX, a line segment XY drawn from vertex X to the midpoint of CB at Y divides triangle CBX into two equal triangles: triangle CXY and triangle BXY.
Thus, Area of triangle BXY = Area CXY 32/2 = 16.
We can visualize that in triangle CXY, line segment RY divides triangle CXY in two equal triangles: triangle RXY and triangle CRY of 16/2=8 units of area.
Again, we can visualize that in triangle CRY, line segment RS divides triangle CRY in two equal triangles: triangle RSY and triangle CRS of 8/2=4 units of area.
Here, in the triangle ABC, a line segment BX drawn from vertex B to the midpoint of AC at X divides triangle ABC into two equal triangles: triangle ABX and triangle CBX.
Thus, Area of triangle CXB = Area ABX = 32.
Again, in the triangle CBX, a line segment XY drawn from vertex X to the midpoint of CB at Y divides triangle CBX into two equal triangles: triangle CXY and triangle BXY.
Thus, Area of triangle BXY = Area CXY 32/2 = 16.
We can visualize that in triangle CXY, line segment RY divides triangle CXY in two equal triangles: triangle RXY and triangle CRY of 16/2=8 units of area.
Again, we can visualize that in triangle CRY, line segment RS divides triangle CRY in two equal triangles: triangle RSY and triangle CRS of 8/2=4 units of area.
gmatclubot
Re: In triangle ABC, point X is the midpoint of side AC and point Y is th [#permalink]
07 Jun 2024, 23:58
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