Question : In a right-angled triangle, if the hypotenuse is 20 cm and the ratio of the other two sides is 4 : 3, the lengths of the sides are:
Option 1: 4 cm and 3 cm
Option 2: 8 cm and 6 cm
Option 3: 12 cm and 9 cm
Option 4: 16 cm and 12 cm
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Correct Answer: 16 cm and 12 cm
Solution : Given: In a right-angled triangle, the hypotenuse is 20 cm and the ratio of the other two sides is 4 : 3. Let the two sides be $4x$ cm and $3x$ cm. Then $(4x)^2+(3x)^2=20^2$ ⇒ $25x^2=400$ ⇒ $x^2=\frac{400}{25}$ ⇒ $x^2=16$ ⇒ $x$ = 4 Therefore, the lengths of the two sides are (4 × 4) = 16 cm and (3 × 4) = 12 cm. Hence, the correct answer is 16 cm and 12 cm.
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