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1. The ratio of the sides of a triangle is 4:6:8. If the perimeter of a triangle is 90 centimeters, what is the length of each side? 2. Tina filled three containers, A, B, and C with orange juice in the ratio 3:4:5. If the total amount of orange juice is 40L, find the capacity of the three containers. 3. A 90-meter stick is cut into 2 pieces given the ratio of 10:20, how long is the shorter stick? The longer stick? 4. A sum of money is to be shared in the ratio 4:6:8. If the smallest share is P10, what are the other two shares? How much money is shared? 5. The total body weight of Jay Jay, Dwayne and Mhadelle is 183 kg. Their weight is in the ratio 4:3:2. What is Jay Jay's weight? How much heavier is Dwayne from Mhadelle?​

Sagot :

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Answer:

1. Let the sides of the triangle be 4x, 6x, and 8x. The perimeter is the sum of the sides, so 4x + 6x + 8x = 90. Simplifying, we get 18x = 90, so x = 5. Therefore, the sides are 4(5) = 20 cm, 6(5) = 30 cm, and 8(5) = 40 cm.

2. Let the capacity of the containers be 3x, 4x, and 5x. The total amount of orange juice is 3x + 4x + 5x = 40L. Simplifying, we get 12x = 40, so x = 40/12 = 10/3. Therefore, the capacities are 3(10/3) = 10L, 4(10/3) = 40/3 ≈ 13.33L, and 5(10/3) = 50/3 ≈ 16.67L.

3. The total length of the stick is 90 meters, so the lengths of the two pieces are 10x and 20x where x is a common multiplier. Since 10x + 20x = 90, we have 30x = 90, so x = 3. Therefore, the shorter stick is 10(3) = 30 meters and the longer stick is 20(3) = 60 meters.

4. Let the shares be 4x, 6x, and 8x. Given that the smallest share is P10, we have 4x = 10, so x = 10/4 = 2.5. Therefore, the shares are 4(2.5) = P10, 6(2.5) = P15, and 8(2.5) = P20. The total amount of money shared is 4 + 15 + 20 = P45.

5. Let Jay Jay's weight be 4x, Dwayne's weight be 3x, and Mhadelle's weight be 2x. Given that the total weight is 183 kg, we have 4x + 3x + 2x = 183. Simplifying, we get 9x = 183, so x = 183/9 = 20.33. Therefore, Jay Jay's weight is 4(20.33) ≈ 81.33 kg. Dwayne is 3(20.33) ≈ 60.99 kg and Mhadelle is 2(20.33) ≈ 40.66 kg. Dwayne is approximately 20.33 kg heavier than Mhadelle.

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