Question

a is equidistant to b and c. find bd. bd = ? b 8x + 5 d 6x + 15 c

Explanation:

Step1: Use property of isosceles triangle

Since \( A \) is equidistant to \( B \) and \( C \), \( \triangle ABC \) is isosceles with \( AB = AC \). Also, \( AD \perp BC \), so \( D \) is the midpoint of \( BC \), meaning \( BD = DC \).
Set \( 8x + 5 = 6x + 15 \).

Step2: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 8x - 6x + 5 = 15 \)
Simplify: \( 2x + 5 = 15 \)
Subtract 5: \( 2x = 15 - 5 = 10 \)
Divide by 2: \( x = \frac{10}{2} = 5 \)

Step3: Find \( BD \)

Substitute \( x = 5 \) into \( BD = 8x + 5 \):
\( BD = 8(5) + 5 = 40 + 5 = 45 \)

Answer:

45