Question

AABC = ADEF. Find the lengths of the given sides.BC = x + 8EF = 3x + 4

Answer 1

It is stated in the problem that triangle ABC is congruent with triangle DEF. By congruence theorem, we can say that sides BC and EF are also congruent. Hence,

`BC\cong EF`

Substitute the algebraic equation constituting the lengths of BC and EF on the equation above, we have

`x+8=3x+4`

Solve for x

`\begin{gathered} 8-4=3x-x \\ 2x=4 \\ x=2 \end{gathered}`

Hence, the measurement of length BC is

`\begin{gathered} BC=x+8 \\ BC=2+8=10 \end{gathered}`

Answer: 10