The legs of an isosceles right triangle have length 12.?

Question

Find the lengths of the hypotenuse and the altitude to the hypotenuse.

Please explain. Thanks a lot.

Answer 1

Ok, you know the pythagorean theorem, right? when you have a right angle triangle with sides a and b coming together in the right angle triangle, a^2 + b^2 =c^2.

So 144 + 144 =c^2

C=the square root of 288.

Now you know the length of all the sides.

Draw a straight line down from the original right angle to the side opposite it. See how you have created 2 new right angle triangles? You already know the length of 2 of the sides of the new triangles, so it will be simple to find the 3rd.

(At least if I understand correctly what they want, that is how you do it.)

Answer 2

A^2 + B^2 = C^2
A and B are the sides so
12^2 + 12^2 = C^2
sqrt 288 = C
C = 16.97

Answer 3

h = sq rt(12^2 + 12^2) = 16.97
The hypotenuse of a right triangle is equal to the square root of the squares of its legs.

Answer 4

h^2 = 2 * 12^2
h^2 = 288
h = 16.97

12^2 = a^2 + (16.97/2)^2
a^2 = 12^2 - 8.49^2
a^2 = 72
a = 8.49