Question

a is equidistant to b and c. find bd. bd =? b 11x + 9 d 4x + 30 c

Explanation:

Step1: Identify the property

Since \( A \) is equidistant to \( B \) and \( C \), triangle \( ABC \) is isosceles with \( AB = AC \). The altitude \( AD \) to the base \( BC \) bisects \( BC \), so \( BD = DC \).

Step2: Set up the equation

Set \( 11x + 9 = 4x + 30 \) (because \( BD = DC \)).

Step3: Solve for \( x \)

Subtract \( 4x \) from both sides: \( 11x - 4x + 9 = 30 \)
Simplify: \( 7x + 9 = 30 \)
Subtract 9 from both sides: \( 7x = 30 - 9 \)
Simplify: \( 7x = 21 \)
Divide by 7: \( x = \frac{21}{7} = 3 \)

Step4: Find \( BD \)

Substitute \( x = 3 \) into \( BD = 11x + 9 \):
\( BD = 11(3) + 9 = 33 + 9 = 42 \)

Answer:

\( 42 \)