Multiple choice

(\triangle ABC \sim \triangle PQR), the areas of (\triangle ABC) and (\triangle PQR) are 64 cm2 and 81 cm2, respectively and AD and PT are the medians of (\triangle ABC) and (\triangle PQR), respectively. If PT = 10.8 cm, then AD = ?

  1. 9

  2. 12

  3. 8.4

  4. 9.6

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For similar triangles, the ratio of areas equals the ratio of squares of corresponding sides or medians. Given areas 64 and 81 cm², the ratio is (8/9)². Therefore, AD/PT = 8/9. With PT = 10.8 cm, AD = (8/9) × 10.8 = 9.6 cm. This property applies to all corresponding linear elements in similar triangles.