1. ## Isosceles Triangle

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?

Thank you!!!

2. Originally Posted by whytechocolate01
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?

Thank you!!!
Hello,

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.

3. Originally Posted by whytechocolate01
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?

Thank you!!!
again, we form two right angled triangles and again we will use Pythagoras' theorem (do you know the theorem?)

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

4. This is what I got...

13 sqrd. = 12 sqrd. + x sqrd

x sqrd = 25

x = 5

Therefore the base = 10

Correct?

5. Yes the total length of the base is 10.

Therefore you are 100% correct