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kifflom [539]
3 years ago
6

| 10. Triangle ABC ~Triangle DEF with AB = 8, BC = 12,

Mathematics
1 answer:
Leno4ka [110]3 years ago
3 0

Answer:

Perimeter of triangle DEF = 54 units

Step-by-step explanation:

Given:

Δ ABC is similar to Δ DEF

AB = 8, BC = 12, AC =16 and DE = 12.

Since, the two triangle are similar, their corresponding sides will be in proportion. Therefore,

\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}

Now, consider the first two ratios.

\frac{AB}{DE}=\frac{BC}{EF}

Plug in 8 for AB, 12 for BC, 12 for DE and solve for EF. This gives,

\frac{8}{12}=\frac{12}{EF}\\8\times EF=12\times 12\\8\times EF=144\\EF=\frac{144}{8}=18

Now, consider the ratio:

\frac{AB}{DE}=\frac{AC}{DF}

Plug in 8 for AB, 16 for AC, 12 for DE and solve for DF. This gives,

\frac{8}{12}=\frac{16}{DF}\\8\times DF=16\times 12\\8\times DF=192\\DF=\frac{192}{8}=24

Therefore, the lengths of sides of triangle DEF are:

DE = 12, EF = 18 and DF = 24

Now, perimeter is the sum of all the sides of the triangle. Therefore,

Perimeter=DE +EF+DF\\Perimeter=12+18+24=54

Therefore, the perimeter of the triangle DEF is 54 units.

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