# Lesson HOW TO solve problems on the isosceles triangle sides measures - Examples

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## How to solve problems on the isosceles triangle sides measures - Examples

In this lesson you will find the solutions of the typical problems that relate to the isosceles triangle sides measures.
Remember that in an isosceles triangle the lateral sides are of equal length.
There are two major approaches, regarding the strategy of the solution.
First, think whether the direct calculations may resolve the problem.
Alternatively, you can consider the solution using the reduction to the some kind of a linear equation.
The examples below show how each of these approaches works.
The Problems 1, 2 and 3 are solved using the direct calculations.
The Problems 4 and 5 are solved using the reduction to the linear equation.

Problem 1
Find the perimeter of the isosceles triangle with the lateral side of 8 cm long and the base of 5 cm long.

Solution
The perimeter of the triangle is the sum of the measures of its sides.
Therefore, in our case the perimeter of the triangle is equal to
2*8 cm + 5 cm = 21 cm.

Answer. The perimeter of the triangle is 21 cm.

Problem 2
Find the perimeter of the isosceles triangle, if its lateral side is 8 cm long and the base is in 4 cm longer.

Solution
The base is 8 cm + 4 cm = 12 cm long in accordance with the problem condition.
The perimeter of the triangle is the sum of the measures of its sides. Therefore, it is equal to
2*8 cm + 12 cm = 28 cm.

Answer. The perimeter of the triangle is 28 cm.

Problem 3
Find the lateral side of the isosceles triangle, if the base is 7 cm long and the perimeter of the triangle is 19 cm.

Solution
The doubled length of the lateral side is 19 cm - 7 cm = 12 cm long in accordance with the problem condition.
Hence, the lateral side is 12/2 = 6 cm long.

Answer. The length of the lateral side of the triangle is 6 cm.

Problem 4
In an isosceles triangle, the lateral side is in 7 cm longer than the base.
Find the measures of the triangle sides, if the perimeter of the triangle is 50 cm.

Solution
Let x be the length of the base of the triangle (in centimeters).
Then the lateral side is x + 7 cm long.
Since the perimeter of the triangle is equal to 50 cm, you can write the equation
x + 2(x +7) = 50.
Simplify this equation step by step and solve it:
x + 2x + 14 = 50,
3x + 14 = 50,
3x = 50 - 14,
3x = 36,
x = 12.

So, the base of the triangle is 12 cm long.
Hence, the lateral side is 12 cm + 7 cm = 19 cm long in accordance with the problem condition.
You can check that the sum of the side measures is equal to the given value of the perimeter:
12 cm + 19 cm + 19 cm = 50 cm.

Answer. The base of the triangle is 12 cm long; the lateral side is 19 cm long.

Problem 5
Find the measures of the isosceles triangle sides, if the lateral side is in two times longer than the base
and the perimeter of the triangle is 30 cm.

Solution
Let x be the length of the base of the triangle (in centimeters).
Then the lateral side is 2x cm long in accordance with the problem condition.
Since the perimeter of the triangle is equal to 30 cm, you can write the equation
x + 2x + 2x = 30.
Simplify this equation and solve it:
5x = 30,
x = 6.

So, the base is 6 cm long.
Hence, the lateral side is of 2*6 cm = 12 cm long in accordance with the problem condition.
You can check that the sum of the side measures is equal to the given value of the perimeter:
6 cm + 2*12 cm = 6 + 24 = 30 cm.

Answer. The triangle base length is 6 cm; the lateral side length is 12 cm.

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