The perimeter of a triangle is 86; find the sides if the middle side is 7 different from each of the two.

| January 19, 2021 | education

In view of the incompleteness of specifying the features of the difference in the lengths of the sides of the triangle, we will analyze two cases:

1) the two sides of the triangle are equal and the third is 7 cm larger than each.

Let x be one of the equal sides of the triangle. Then the third side is equal to (x + 7) cm, the second is also equal to x cm.Since the perimeter is 86 cm, we obtain and solve the equation:

x + x + x + 7 = 86;

3 * x = 79;

x = 26 1/3 cm. The second side is 26 1/3 cm. The third is 33 1/3 cm.

2) the sides are different. Let x be the smallest side of the triangle. Then (x + 7) is the second side, (x + 14) is the third. We get the equation:

x + x + 7 + x + 14 = 86;

3 * x = 65;

x = 21 2/3 cm.

Then the second side is 28 2/3 cm, the third is 35 2/3 cm.



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