Best Answer:
Okay, so in this problem, you know that two of the sides are 13 cm, because an isosceles triangle has two equal sides, and they tell you that one is 13 cm.

So the perimeter is 13cm + 13cm + x = 50cm, where x is the length of the other side. Solve for x:

26 cm + x = 50 cm

x = 50cm - 26 cm = 24 cm

So, if we look at the triangle with the two equal 13cm sides on the left and right, while the 24 cm side is at the bottom, then we can find the area with the formula for area of a triangle:

Area of triangle = (1/2)Base * Height

The way we have the triangle set up, the base is 24 cm. To find the height, we'll have to use some geometry.

If we split the triangle in half vertically down the middle, we're left with two right triangles with hypotenuse 13cm and the base is (24/2).

To find the height we can use Pythagorean Theorem which is:

A² + B² = C²

Where C is the hypotenuse of a right triangle, and A and B are the sides.

We know C = 13, and we know one of the sides is (24/2)

Plug these values in and solve for the other leg, which is the height of our Isosceles triangle.

13² = 12² + B²

13² - 12² = B²

B = √ (13² - 12²)

B = 5 cm

Now plug them all into the area formula:

A = (1/2)Base * Height

(1/2)*24cm * 5cm = 120 cm²

Hope this helps!

Source(s):