Question

Find the value of x in the isosceles triangle shown below. A.) x=10 B.) x=48 C.) x= square root of 80 D.) x=square root of 96

Answer 1

Notice that we are dealing with an isosceles triangle, which means that the sides labeled as x are equal, and not just that, but that the height segment (shown of length 8) divides the base of the triangle in two equal segments, since it is the median of the triangle .

Then, the height of the triangle is dividing the original isosceles triangle in TWO EQUAL right angle triangles.

We can use the Pythagorean theorem with the two right angle triangles, noting that we want to find the size of the HYPOTENUSE in the triangles (x) and that we know the size of the two legs:

One leg = 8 and the other leg = 12 / 2 = 6

Then we use the Pytagorean theorem as shown below:

`\text{hypotenuse}=\sqrt[]{8^2+6^2}=\sqrt[]{64+36}=\sqrt[]{100}=10`

Therefore, x must measure 10 units. Then, please select answer labeled A in your list.