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

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,

Now, consider the first two ratios.

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

Now, consider the ratio:

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

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,

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

step-by-step explanation: