Mathematics, 16.12.2019 08:31 michaelwthms

|10. triangle abc ~triangle def with ab = 8, bc = 12,
ac = 16, and de = 12. what is the
perimeter of adef?

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Answer from: mccdp55

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.

Answer from: Quest

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the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights

Answer from: Quest

Photo math will give you the step by step answer : )

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