Question

In ΔАВC; the mid-points of the sides BC, CA and AB are D, E and F respectively. The ratio of ar (ΔDEF) and ar (ΔABC) is ______.

Options

• 1 : 4

• 1 : 3

• 1 : 2

• 1 : 1

Answer 1

In ΔАВC; the mid-points of the sides BC, CA and AB are D, E and F respectively. The ratio of ar (ΔDEF) and ar (ΔABC) is 1 : 4.

Explanation:

D, E, F are midpoints, so DE, EF and FD are each parallel to and half the corresponding sides of ΔABC midpoint theorem.

Hence, ΔDEF is similar to ΔABC with linear scale `1/2`.

Area scales as the square of linear scale.

So, area (ΔDEF) : area (ΔABC) = `(1/2)^2 = 1/4`.