Question : The sides of a triangle are in the ratio 7 : 9 : 12. The difference between the lengths of the largest and smallest sides is 15 cm. The length of the largest side would be (in cm):
Option 1: 36
Option 2: 12
Option 3: 60
Option 4: 24
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Correct Answer: 36
Solution : Given: The sides of a triangle are in the ratio of 7 : 9 : 12. Let the sides of the triangle be $7x, 9x$, and $12x$. According to the question, $12x -7x = 15$ ⇒ $5x = 15$ ⇒ $x = \frac{15}{5} = 3$ Largest side $=12x = 12 × 3= 36$ cm Hence, the correct answer is 36.
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Question : The lengths of the two sides of a triangle are 14 cm and 9 cm. Which of the options below can be the length of the third side?
Option 1: 17 cm
Option 2: 23 cm
Option 3: 24 cm
Option 4: 5 cm
Question : The median of an equilateral triangle is $15 \sqrt{3} \mathrm{~cm}$. What is the side of this triangle?
Option 1: 24 cm
Option 2: 18 cm
Option 3: 30 cm
Option 4: 36 cm
Question : The lengths of the two sides adjacent to the right angle of a right-angled triangle are 1.6 cm and 6.3 cm. Find the length of the hypotenuse.
Option 1: 6.7 cm
Option 2: 7.5 cm
Option 3: 6.5 cm
Option 4: 7 cm
Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:
Option 1: 9 cm
Option 2: 13 cm
Option 3: 3 cm
Option 4: 6 cm
Question : The sides of a triangle are of length 8 cm, 15 cm, and 17 cm. Find the area of the triangle.
Option 1: 65 cm2
Option 2: 75 cm2
Option 3: 60 cm2
Option 4: 70 cm2
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