Let A, B, C be the mid-points of sides PQ, QR PR, respectively, of ?PQR If the area of ?PQR is 32 cm2, then find the area of ? ABC.
This questions was previously asked in
Combined Graduate Level Examination Tier I 2023
Explanation:
- Triangle \( \triangle PQR \) has midpoints A, B, and C on sides PQ, QR, and PR.
- The area of \( \triangle PQR \) is given as 32 cm².
- According to the Midpoint Theorem, \(\triangle ABC\) will be similar to \(\triangle PQR\) and half in both dimensions.
- The area of \(\triangle ABC\) is thus \(\frac{1}{4}\) of the area of \(\triangle PQR\) because area scales with the square of the linear dimensions.
- Therefore, the area of \(\triangle ABC\) is \(\frac{1}{4} \times 32\) cm² = 8 cm².
- Option 4: 8 cm² is the correct answer.
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By: Parvesh Mehta