The lengths of the sides of a triangle are in the ratios 2 : 6 : 7The length of the longest side of the triangle is 24.5 cm.Work out the perimeter of the triangle.
Question
The lengths of the sides of a triangle are in the ratios 2 : 6 : 7The length of the longest side of the triangle is 24.5 cm.Work out the perimeter of the triangle.
Solution
To solve this problem, we first need to understand that the sides of the triangle are proportional to the ratios given.
Step 1: Add the ratios together. 2 + 6 + 7 = 15
Step 2: The longest side of the triangle is given as 24.5 cm, which corresponds to the ratio 7. To find the equivalent of ratio 1, we divide the length of the longest side by 7. So, 24.5 cm / 7 = 3.5 cm.
Step 3: Now that we know the equivalent of ratio 1, we can find the lengths of the other sides. The side corresponding to the ratio 2 is 2 * 3.5 cm = 7 cm. The side corresponding to the ratio 6 is 6 * 3.5 cm = 21 cm.
Step 4: To find the perimeter of the triangle, we add up the lengths of all the sides. So, 7 cm + 21 cm + 24.5 cm = 52.5 cm.
Therefore, the perimeter of the triangle is 52.5 cm.
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