# The lengths of the sides of the triangle are 6: 5: 7 and the sum of the lengths of the longest

The lengths of the sides of the triangle are 6: 5: 7 and the sum of the lengths of the longest and the smallest sides is 24 cm. Find the perimeter of this triangle.

Let the smaller side of our triangle be defined through the expression 5a.

Therefore, it will be possible to represent the larger side using the expression 7a.

But after all, from the condition of our task, we know for sure that the sum of their lengths is 24, so we can write down the equation and, having solved it, find the length of the third side:

7a + 5a = 24;

12a = 24;

a = 2;

6 * 2 = 12.

Now we can determine what the perimeter of this triangle will be:

12 + 24 = 36.

Answer: The perimeter will be 36 cm.

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