Question

5. An isosceles triangle is shown below with side lengths of 12 and a base length of 20. If a line segment AD is drawn from A to side BC such that D lies on BC and AD 1 BC then find the length of AD in simplest radical form.

Answer 1

To find the length of AD in the given isosceles triangle, you can use the Pythagorean theorem. The length of AD in simplest radical form is √244.

Step-by-step explanation:

To find the length of AD in the given isosceles triangle, we can use the Pythagorean theorem. In this case, side AD is the hypotenuse of the right triangle. The legs of the right triangle are the half of the base length, since the triangle is isosceles. Therefore, the legs are 20/2 = 10.

Using the Pythagorean theorem, we can find the length of AD as follows:

AD2 = 102 + 122

AD2 = 100 + 144

AD2 = 244

Taking the square root of both sides, we get:

AD = √244

Therefore, the length of AD in simplest radical form is √244.

Answer 2

AD = 16

Step-by-step explanation:

Using the Pythagorean Theorem:

A2 + D2 = C2

122 + D2 = 202

144 + D2 = 400

D2 = 256

D = 256 = 16