Find the ratio of area of the triangles ABC and PQR such that AB = BC=CA = 6m each and PQ, QR, RP are half of the sides AB BC and CA respectively?

Answer 1

Since the sides of triangle are equal, the triangles are equilateral.

Just for your information, in this question, we do not require the length of sides. It is just additional information. :)

The area of equilateral triangle is:

(√3)/4 × a², where a is the side of the equilateral triangle.

For triangle ABC, area will be = (√3)/4 × a² (Let 'a' is the side of triangle ABC)

Since, side of triangle PQR is half that of ABC, it will be = a/2

Therefore, area of triangle PQR = (√3)/4 × (a/2)² = (√3)/16 × a²

Take the ratio of areas of triangle ABC and PQR:

[(√3)/4 × a²] / [(√3)/16 × a²] = 4:1

Answer 2

15.58/3.89