Question

Points B and C lie on line segment AD, with AB < AC. If AD = 76, CD = 24 and AB = BC, what is the value of BC?

Answer 1

ANSWER

$BC=26$

EXPLANATION

First, let us make a sketch of the problem:

Since AB is equal in length to BC, they both have a value of x.

The total length of AD is 76. This implies that:

$\begin{gathered} AB+BC+CD=AD \\ x+x+24=76 \end{gathered}$

Solve for x by simplifying the equation above:

$\begin{gathered} 2x+24=76 \\ 2x=76-24=52 \\ \\ x=\frac{52}{2} \\ \\ x=26 \end{gathered}$

Therefore, the value of BC is:

$BC=26$

That is the answer.