Question

| 10. Triangle ABC ~Triangle DEF with AB = 8, BC = 12,
AC = 16, and DE = 12. What is the
perimeter of ADEF?

Answer 1

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.