Question

in the figure shown below, the length of \\(\overline{ac}\\) is 35 meters. what is the length, in meters, of \\(\overline{bc}\\) ?
a ----3x---- b ----2x + 5---- c

Explanation:

Step1: Set up the equation for AC

Since \( AC = AB + BC \), and \( AB = 3x \), \( BC = 2x + 5 \), \( AC = 35 \), we have \( 3x + (2x + 5) = 35 \).

Step2: Solve for x

Simplify the left side: \( 5x + 5 = 35 \). Subtract 5 from both sides: \( 5x = 30 \). Divide by 5: \( x = 6 \).

Step3: Calculate BC

Substitute \( x = 6 \) into \( BC = 2x + 5 \): \( 2(6) + 5 = 12 + 5 = 17 \).

Answer:

17