The legs of an isosceles triangle are 13 units long and the altitude to the base is 12 units long. What is the length of the base? How do you solve this?
the altitude divides the triangle into 2 right triangles. The legs of the isosceles triangle are the hypotenuses of the 2 right triangles and x is half of the base and it is one leg of a right triangle.
Now use Pythagorean theorem:
13² = 12² + x² ==> x² = 25 ==> x = 5
Therefore the base is 10 units long.
for one of the triangles we would have the base unknown, the height = 12 and the hypotenuse = 13. use Pythagoras' theorem to find the base. this base will be half the base of the whole tirangle, so just multiply the answer by 2 and there you have it