In the figure below, the lengths of right triangle BAC are shown. Side BD bisects side AC. What is the length of side CD ?

A.) √3

B.) 2

C.) 3

D.) 2√5

E.) 4

B.) 2

C.) 3

D.) 2√5

E.) 4

Use the Pythagorean Theorem in triangle BAC to find side AD which is congruent to side CD, since BD bisects AC.

4² + b² = 5² {substituted legs and hypotenuse into Pythagorean Theorem}

16 + b² = 25 {evaluated exponents}

b² = 9 {subtracted 16 from each side}

b = 3 {took positive square root of each side}

**{sum of the squares of the legs, a and b, is equal to the square of the hypotenuse}**

a² + b² = c²__Pythagorean Theorem__a² + b² = c²

4² + b² = 5² {substituted legs and hypotenuse into Pythagorean Theorem}

16 + b² = 25 {evaluated exponents}

b² = 9 {subtracted 16 from each side}

b = 3 {took positive square root of each side}

**C.) 3****Ask Algebra House**