What is AB^{2}+4BQ^{2} equal to?
Consider the following for the next three (03) items that follow: ABC is a triangle with AB=1.6\text{ cm}, BC=6.3\text{ cm} and CA=6.5\text{ cm}. Let P and Q be the mid-points of AB and BC respectively.
- A. 41.25\text{ cm}^{2}
- B. 42.25\text{ cm}^{2} ✓
- C. 43.75\text{ cm}^{2}
- D. 44.25\text{ cm}^{2}
Correct Answer: B. 42.25\text{ cm}^{2}
Explanation
Notice that 1.6^2 + 6.3^2 = 2.56 + 39.69 = 42.25 = 6.5^2, so \triangle ABC is right-angled at B. Since Q is the midpoint of BC, BC = 2BQ \implies BC^2 = 4BQ^2. Thus, AB^2 + 4BQ^2 = AB^2 + BC^2 = AC^2 = 6.5^2 = 42.25\text{ cm}^2.
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