In an isosceles triangle, the perimeter is 75 cm and one of the sides is 25 cm. Find all its sides. Can you find all angles of the triangle? Explain your answer.

By looking at this information, we can tell easily that this triangle in the problem is an equilateral triangle. Now, most of you are probably thinking, "But an equilateral triangle isn't an isosceles triangle???" However, that statement is wrong, because the definition of an isosceles triangle is that 2 sides at minimum have to be congruent. Now that we have that covered up, let me tell you why it is an equilateral triangle. The perimeter is 75 and one of the sides is 25, right? If it is supposed to be an isosceles triangle, this means that there are two possibilities- 1, there must be at least 2 sides that equal 25, or 2, the other two sides are equal to each other. In any case, we see this combination of side lengths both times- 25, 25, 25. Let me explain. For the first case, if we want 2 sides to equal 25, the last side should be 75-25-25, which equals 25. We get our combination. For the 2nd scenario, 75-25=50, so the other sides should be in total 50 cm. Since the other sides have to be equal to each other, 50/2 should equal each of the 2 sides. They are 25. So again, we get this combination of 25, 25, 25. Now, the angle finding part is very easy. Since the measurements of this triangle are 25cm, 25cm, 25cm, this is an equilateral triangle, meaning each of its angle measurements are 60 degrees.

Cheers!

what about angles?

You just gotta add the degree sign

To find all the sides of the isosceles triangle, we need to understand that in an isosceles triangle, two sides are equal in length. Let's call the length of the equal sides of the triangle as "x."

Given that the perimeter of the triangle is 75 cm, we can write the equation:
x + x + 25 = 75

Simplifying the equation:
2x + 25 = 75
2x = 75 - 25
2x = 50
x = 50 / 2
x = 25

So, the length of the equal sides (x) is 25 cm, and the length of the other side (the base) is also 25 cm.

Now, let's find the angles of the isosceles triangle. Since the two equal sides are of length 25 cm, the opposite angles formed by these two sides are also equal. Let's call these angles as "A."

We also know that the sum of the interior angles of any triangle is 180 degrees. In our triangle, we have two equal angles (A) and one angle on the base (let's call it angle "B"), which means we have:

A + A + B = 180

Since A and B represent angles, we can see that:
2A + B = 180

Now, to find the values of A and B, we need more information. With the given information (perimeter and one side length), we cannot determine the values of angles A and B uniquely.

So, we cannot find all the angles of the triangle without additional information.

wait no its not

75-25 = 50

It looks like the sides are 25, 25, 25 so it is really equilateral.

If I thought that the side given 25 had the equal side then it would be 25 with 25 left over for the other side.

If I thought the given side, didn't have an equal side, I would have subtracted 25 and divided by 2 like I did originally.

Equilateral triangles have equal sides and equal angles. So.. each angle must be 60 degrees.

Its wrong