Q.43
Let XYZ be an equilateral triangle and let P, Q, R be the mid points of YZ, XZ, and XY, respectively.
Let r = Area(∆PQR)Area(∆XYZ).
The value of r is _______.
Introduction
When P, Q, and R are the midpoints of the sides of an equilateral triangle XYZ, the triangle PQR is called the medial triangle, and it is always similar to the original triangle. In this article, the goal is to compute the ratio of the area of triangle PQR to the area of triangle XYZ and understand each step using the midpoint theorem and properties of similar triangles.
Problem restatement
XYZ is an equilateral triangle.
P, Q, R are midpoints of YZ, XZ, XY respectively.
Define r = Area(△PQR) / Area(△XYZ)
Find the value of r.
Although the question is fill-in-the-blank, the reasoning works the same way as for a multiple-choice problem, and each potential
