Question

a is equidistant to b and c. find bd. bd = ? the triangle has ab and ac marked as equal, ad is perpendicular to bc, bd is 8x + 5, dc is 6x + 15.

Explanation:

Step1: Identify the property

Since A is equidistant to B and C, and AD is perpendicular to BC, triangle ABC is isosceles with AB = AC. In an isosceles triangle, the perpendicular from the apex (A) to the base (BC) bisects the base. So, BD = DC.

Step2: Set up the equation

Set \( 8x + 5 = 6x + 15 \)

Step3: Solve for x

Subtract \( 6x \) from both sides: \( 2x + 5 = 15 \)
Subtract 5 from both sides: \( 2x = 10 \)
Divide by 2: \( x = 5 \)

Step4: Find BD

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

Answer:

45