The perimeter of two equalater triangles are in ration 2:3. If the perimeter of the smaller triangle is 16 cm what is the measure of a side of the larger triangle?
2/3 = 16/x
2x = 48
x = 24
24/3 = ?
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To solve this problem, we can use the concept of ratios and proportions. Here's how you can find the measure of a side of the larger equilateral triangle:
1. Start by setting up the ratio of the perimeters. Given that the ratio of the perimeters of the two equilateral triangles is 2:3, we can represent it as 2x:3x, where x is a common factor.
2. Since the perimeter of the smaller triangle is given as 16 cm, we can equate it to 2x: 2x = 16 cm. Solve for x by dividing both sides by 2: x = 8 cm.
3. Now that we have the value of x, we can find the perimeter of the larger triangle. The perimeter of the larger triangle is 3x, which equals 3 * 8 cm = 24 cm.
4. Finally, as an equilateral triangle has all sides equal, each side of the larger triangle will be equal to the perimeter divided by 3: 24 cm / 3 = 8 cm.
Therefore, the measure of a side of the larger equilateral triangle is 8 cm.