Question
A circle is inscribed in a triangle ABC with sides 12
cm, 16 cm, and 20 cm. What is the radius of the circle?Solution
The triangle is a right triangle with sides in a 3:4:5 ratio. The area A = (1/2) × base × height = (1/2) × 12 × 16 = 96 cm². The semiperimeter s = (12 + 16 + 20) / 2 = 24 cm. The inradius r = A / s = 96 / 24 = 4 cm. Correct answer: c) 4 cm
- Ravi and Raj entered into a business where Ravi invested Rs. 9,000. Raj withdrew his capital after 6 months. If their profit ratio at the end of the year w...
‘P’ invested Rs. 30000 in a business. ‘Q’ joined after ‘x’ months with an investment of Rs. 10000 less than ‘P’. If the ratio of the pro...
Three friends A, B and C entered into partnership by investing Rs. 15X, Rs. (3X + 26) and Rs. (1000 – 6X) respectively. The ratio of the time period o...
A, B and C invested in partnership. A invest Rs.5000 for 4 months, B invests Rs.2000 for 2 months and C invests Rs.8000 for 2 months. C is working partn...
A and B started a business by investing Rs.5000 and Rs.8000 respectively. After 4 months A withdrew 40% of his investment. If at the end of the year, pr...
A and B started a retail store with initial investments in the ratio 6:7 and their annual profits were in the ratio 4:5. If A invested the money for 7 m...
A and B started a business. After 3 years they received Rs 1245 as profit in which A's share is Rs 720, then find the ratio of investment of A and B.
- Aman and Bhanu started a business with initial investments of Rs. 1824 and Rs. 1248, respectively. After 7 months, Aman increased his investment by Rs. 330...
Amit and Anil started a business together such that Amit’s investment is Rs. 2,000 more than Anil’s. Anil left the business after 6 months. If the r...
A and B entered into a business investing their capital in the ratio of 16:21, respectively and the respective ratio of time for which they made their i...
