MATH SOLVE

9 months ago

Q:
# triangles ABC and DEF are similar. The lengths of the sides of ABC are 140,120, and 110. The length of the smallest side of DEF is 260, what is the length of the longest side of DEF?

Accepted Solution

A:

Answer:The longest side is 330.9 units.Step-by-step explanation:Since the triangles are similar, the ratio of the corresponding sides of two triangles is equal.In other words,[tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}[/tex]The lengths of the sides of triangle ABC are AB = 140 , BC = 120 , CA = 110The length of smallest side of triangle DEF is 260.Thus, [tex]\frac{CA}{FD} = \frac{110}{260} = \frac{11}{26}[/tex]thus,[tex]\frac{AB}{DE} = \frac{11}{26} = \frac{140}{DE}[/tex]So, DE = 330.9 unitssimilarly, [tex]\frac{BC}{EF} = \frac{11}{26} = \frac{120}{EF}[/tex]So, EF = 283.636 unitsThus the sides of triangle are 260, 283.636 and 330.9 units.The longest side is 330.9 units.