Question

In the figure, ∆ABC~∆XYZ. What is the perimeter of ∆ABC? Show your work.

Answer 1

Answer:

49 units

Step-by-step explanation:

Given the triangles are similar then the ratios of corresponding sides are equal, that is

$\frac{BC}{YZ}$ = $\frac{AB}{XY}$, substitute values

$\frac{BC}{44}$ = $\frac{11}{22}$ ( cross- multiply )

22BC = 484 ( divide both sides by 22 )

BC = 22

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Similarly

$\frac{AC}{XZ}$ = $\frac{AB}{XY}$, substitute values

$\frac{AC}{32}$ = $\frac{11}{22}$ ( cross- multiply )

22AC = 352 ( divide both sides by 22 )

AC = 16

Thus perimeter of Δ ABC is

perimeter = AB + BC + AC = 11 + 22 + 16 = 49 units