# The perimeter of an isosceles triangle is 18cm. What are its sides equal to if the base is 8cm?

March 28, 2021 | education

| The perimeter of a triangle is the sum of the lengths of all its sides, we write the formula:

P = a + b + c.

An isosceles triangle has two sides equal – by definition.

Therefore, if the perimeter and length of the side lying at the base are known (while the side ones are equal), we derive the formula:

P = 2a + c;

Substitute the data we know and find the double product of equal sides:

2a = P – c;

2a = 18 – 8;

2a = 10.

Now let’s find the length of one side:

a = 10: 2;

a = 5.

Thus, the sides are equal to 5 centimeters.

Answer: a = 5 centimeters; h = 5 centimeters.

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