Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is
The line joining the midpoints of the sides of the triangle form four triangles, each of which is similar to the original triangle.
ΔABC ~ ΔPQR
In ΔABC, P and R are mid points of AB and AC respectively.
PR || BC (midpoint theorem)
In ΔABC and ΔAPR
∠A is common and ∠APR = ∠ABC (corresponding angles)
Therefore, ΔABC ~ ΔAPR (AA similarity)
In ΔABC and ΔPQR, since P, Q, R are the midpoints of AB, BC and AC respectively,
PR = ½BC; (midpoint theorem)
ΔABC ~ ΔPQR (SSS similarity)
Area(ΔPQR) / Area(ΔABC) = PR2/BC2 = (1/2)2 = 1/4
Area(ΔPQR) = Area(ΔABC)/4 = 5/4
The correct option is C.