Question

In a triangle, the middle-length side is 3 more than the shortest side, and the longest side is double the middle-length side. The perimeter of the triangle is 45 cm. Find the lengths of the sides. a) Shortest side: 12 cm, Middle-length side: 15 cm, Longest side: 30 cm b) Shortest side: 9 cm, Middle-length side: 12 cm, Longest side: 24 cm c) Shortest side: 15 cm, Middle-length side: 18 cm, Longest side: 36 cm d) Shortest side: 10 cm, Middle-length side: 13 cm, Longest side: 26 cm

Answer 1

To find the lengths of the sides of the triangle, we can create and solve an equation using the given information.

Step-by-step explanation:

To solve this problem, let's assign variables to the lengths of the sides of the triangle. Let x be the shortest side, x+3 be the middle-length side, and 2(x+3) be the longest side. We can now set up an equation using the given information: x + (x+3) + 2(x+3) = 45. Simplifying, we have 4x + 9 = 45. Subtracting 9 from both sides, we get 4x = 36. Dividing by 4, we find that x = 9. Therefore, the lengths of the sides are: shortest side = 9 cm, middle-length side = 12 cm, longest side = 24 cm.

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