Question

8.) Triangle ABC is a right triangle with Angle B being the right angle AB = 8 and BC = 6 Segment AC has a midpoint M. AM = 2x + 1 Solve for x.

Answer 1

Explanation:

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem. Since triangle ABC is a right triangle with AB = 8 and BC = 6, we can use the Pythagorean theorem to find the length of AC:

AC2=AB2+BC2

AC2=82+62

AC2=64+36

AC2=100

AC=100​

AC=10

Since M is the midpoint of AC, AM = MC. We are given that AM = 2x + 1, so MC = 2x + 1. Since AC = AM + MC, we can substitute the values we know to find x:

AC=AM+MC

10=(2x+1)+(2x+1)

10=4x+2

8=4x

x=48​

x=2

So, x is equal to 2.