Question

a is equidistant to b and c.
find bd.
bd = ?
b 3x + 5 d 7x - 3 c

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 altitude from the apex (A) to the base (BC) bisects the base. So, BD = DC.

Step2: Set up the equation

Given BD = \(3x + 5\) and DC = \(7x - 3\), we set them equal: \(3x + 5 = 7x - 3\).

Step3: Solve for x

Subtract \(3x\) from both sides: \(5 = 4x - 3\). Add 3 to both sides: \(8 = 4x\). Divide by 4: \(x = 2\).

Step4: Find BD

Substitute \(x = 2\) into BD's expression: \(3(2) + 5 = 6 + 5 = 11\).

Answer:

11