Isosceles Triangle

[NMencia09]

What is the minimum amount of information that you need to find the height and area of an isosceles triangle?

You know 2 sides are equal, and if you cut the isosceles down the middle you form 2 right triangles.

So if you know one of the equal sides, and the base, you can find the height. But you need at least that much information.

Is this right?

thanks

[jnelson0612]

What is the minimum amount of information that you need to find the height and area of an isosceles triangle?

You know 2 sides are equal, and if you cut the isosceles down the middle you form 2 right triangles.

So if you know one of the equal sides, and the base, you can find the height. But you need at least that much information.

Is this right?

thanks

Correct, UNLESS it happens to be an equilateral triangle (which is also classified as isosceles, because it has at least two sides equal). Then once we draw the line splitting the triangle in half we have a 30-60-90 triangle. In this situation we only need one measure to be able to determine the others, because a 30-60-90 triangle maps its angles to side lengths x-xsqrt3-2x, and any side length is sufficient to determine the others.

The other possibility is a 45-45-90 triangle, with the hypoteneuse serving as the base. When I draw the line splitting the triangle here, I create two 45-45-90 triangles. Again, only one measure would suffice, because a 45-45-90 triangle maps its angles to side lengths of x-x-xsqrt2.