The hypotenuse AC of a right-angled ABC is 3√5 cm. If AB is doubled and BC is tripled such that ABC remains a right-angled triangle, the hypotenuse becomes 15 cm. What is AB + BC equal to?
A.10 cm
B.9 cm✓ Correct
C.2√5 cm
D.8 cm
Explanation
AB² + BC² = 45. (2AB)² + (3BC)² = 225 ⟹ 4AB² + 9BC² = 225. From first: AB² = 45−BC². Substitute: 4(45−BC²)+9BC² = 225 ⟹ 180+5BC² = 225 ⟹ BC² = 9, BC = 3. AB² = 36, AB = 6. Sum = 9 cm.
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