2018 Question Paper Solution | Question 6

This is an easy 1-mark question from the chapter Triangles. Concept tested: Computing ratio of areas of two similar triangles when the ratio of the corresponding sides of the two triangles are given.

Question 6: Given ∆ ABC is similar to ∆ PQR. If \\frac{AB}{PQ} = \frac{1}{3}), then find \\frac{ar ∆ ABC}{ar ∆ PQR})

Video Explanation

Explanatory Answer | Q6 2018 Board Paper

Theorem: Ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides.

\\frac{\text{Area of Δ ABC}}{\text{Area of Δ PQR}}) = \\frac{\text{Square of corresponding side of ABC}}{\text{Square of corresponding side of PQR}}) = \\frac{{AB}^2}{{PQ}^2})
\\frac{\text{Area of Δ ABC}}{\text{Area of Δ PQR}}) = \\frac{{AB}^2}{{PQ}^2}) = \\frac{1^2}{3^2}) = \\frac{1}{9})