Dan is an isosceles triangle. So the two sides of him are equal. And the third party will be the basis.

Now it is known that one of the parties is more than the other 4 times.

Since the sides are equal, 2 cases are possible:

**1)** The base is 4 times larger. But in this case it will not work to get a triangle.

Let the side side of the X and the other side side x, then the base is 4x

But then the sum of the side sides x+x < 4x, and in the inequality of the triangle: the sum of the two sides should be more than the third side.

You can imagine visually: the long side in the base and along the edges try short (4 times smaller) to twist on the tops and they cannot be connected in any way

**2)** The side side is 4 times more than the base. Let the base x, then the side are 4x

Then the perimeter (the sum of all sides)

X+4x+4x = 45

9x = 45

X = 5 cm

Side sides do not ask (but they will be 20 cm)

**Answer: base = 5 cm**

If I’m not mistaken, then children teach the topic about isosceles triangles in grade 7 on geometry. But there is nothing complicated in it.

And so, we know that the isosceled triangles are equal to the side sides, respectively, the third will be less than the other two (clear from the conditions of the problem). To solve, we will compose an equation:

4x+4x+x = 45

9x = 45

X = 5

It turns out two sides of the triangle 20 cm, and the base is 5 cm.

So I coped with this task.

Correct my answer. Something with these Olympiads the brain is tired)

In an isosceles triangle, the side sides are equal.

Let x cm – the length of the same side sides of the triangle, then 4 cm – the length of the base. But this option is impossible, since the triangle has the sum of two sides more than a third side, and we will get x+x<4x

So, the side side is greater than the base, then the base x cm, and the side storm – 4x cm. Then we get an equation:

4x+4x+x = 45

9x = 45

x = 5 cm – base.

Answer: The base of the triangle is 5 cm.

**Condition**:

An isosceles triangle with a perimeter of 45cm. The attitude of the parties is 4 to 1. We determine what the base of this triangle is equal.

**Solution**:

In an isosceles triangle, two sides have an equal length.

If one of the parties is 4 times larger, then (and the base of an isosceles triangle cannot be longer than the side) the smaller side is the base.

x is the length of the base, 4x – each side of the owl -eater triangle.

The perimeter of this triangle is 45cm.

Of these conditions, we compile the equation:

4x+4x+x = 45

9x = 45

x = 5 cm – the base of the triangle.

Answer: The base of the isosceles triangle is 5cm.

The ratio of the sides of the isosceles triangle, like 4: 1: 1, does not pass, the ratio of the sides remains, like 4: 4: 1, only five parts.

One part (just the desired foundation of an isosceles triangle) will be:

45cm / 5 = 9cm

Answer: 9cm