# The lateral side of an isosceles triangle is twice the length of the base, and the perimeter

The lateral side of an isosceles triangle is twice the length of the base, and the perimeter of the triangle is 75cm. Calculate the lengths of all the midlines of the triangle.

An isosceles triangle has two equal lateral sides. Let x cm be the length of the base of an isosceles triangle, then 2x cm is the length of its lateral side. Based on the data of the problem, as well as the given designations, we will compose an equation and solve it:

2x + 2x + x = 75,

5x = 75,

x = 75/5,

x = 15 cm.

We found the length of the base of the triangle. Let’s find its sides:

15 * 2 = 30 cm.

The middle line connects the midpoints of the two sides and is parallel to the third. It is equal to half of the third side. The middle lines parallel to the sides are equal to each other. Let’s find their meaning:

30/2 = 15 cm.

Find the middle line parallel to the base:

15/2 = 7.5 cm.

Answer: The midlines parallel to the sides of an isosceles triangle are 15 cm, the midline parallel to the base is 7.5 cm.

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