One of the sides of a triangular isosceles triangle is 15cm smaller than the other

| January 29, 2021 | education

One of the sides of a triangular isosceles triangle is 15cm smaller than the other, find all sides of the triangle if its perimeter is 75cm.

Let us denote by c the length of that of the two given sides of this isosceles triangle, which is shorter.

Then the other side of this triangle should be equal to + 15 cm.

Let’s consider two cases.

1) Side c is the side of this triangle.

Then the length of the second side side should also be equal to c cm, and the length of the base – c + 15 cm.

Since the perimeter of the triangle is 75 cm, we can make the following equation:

c + c + c + 15 = 75,

solving which, we get:

3s + 15 = 75;

c + 5 = 25;

c = 25 – 5 = 20 cm.

Therefore, in this case, the lengths of the sides of the triangle are 20 cm, 20 cm and 20 + 15 = 35 cm.

2) Side with is the base of this triangle.

Then the lengths of the sides are equal to + 15 cm, and since the perimeter of the triangle is 75 cm, we can draw up the following equation:

s + s + 15 + s + 15 = 75,

solving which, we get:

3s + 30 = 75;

c + 10 = 25;

c = 25 – 10 = 15 cm.

Therefore, in this case, the lengths of the sides of the triangle are 15 cm, 30 cm and 30 cm.

Answer: I satisfy the conditions of the problem with a triangle with sides of 20 cm, 20 cm and 35 cm and a triangle with sides of 15 cm, 30 cm and 30 cm.



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