Mathematics

Problem

Two triangles

\triangle ABC

and

\triangle DEF

have the following measurements:

AB = 6.5\text{ cm},\; AC = 4.5\text{ cm},\; \angle A = 60^{\circ}

DE = 6.5\text{ cm},\; DF = 4.5\text{ cm},\; \angle D = 60^{\circ},\; EF = 7\text{ cm}

Let

BC = x\text{ cm}

. Answer the questions below. a. Are the two triangles congruent? Give a suitable reason based on the given data. b. Determine the value of

x

. Show all steps. c. Calculate the perimeter of

\triangle ABC

. Write the answer with proper units.