Question

Answer the question in the picture.

Answer 1

AC=AB+BC

AC=6+r

AD=12

DC=r

by Pythagorus theorem

AC*2=AD*2+DC*2

(6+r)*2=12*2+r*2

36+12r+r*2=144+r*2

12r+r*2-r*2=144-36

12r=108

r=108/12

r=9

Answer 2

r=9

Explanation:

We can use the Pythagorean to solve, since this is a right triangle

The leg lengths are r and 12

The hypotenuse is (r+6)

a^2 + b^2 = c^2

r^2 + 12^2 = (r+6)^2

Foiling out the right hand side

(r+6)(r+6_ = r^2+6r+6r+36

r^2 +144 = r^2 +12r+36

Subtracting r^2 from each side

r^2-r^2 +144 = r^2-r^2 +12r+36

144 = 12r+36

Subtract 36 from each side

144-36 = 12r+36-36

108 = 12r

Divide each side by 12

108/12 = 12r/12

9=r