Question

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

Answer 1

49 units

Explanation:

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

`(BC)/(YZ)` =
`(AB)/(XY)`, substitute values

`(BC)/(44)` =
`(11)/(22)` ( cross- multiply )

22BC = 484 ( divide both sides by 22 )

BC = 22

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Similarly

`(AC)/(XZ)` =
`(AB)/(XY)`, substitute values

`(AC)/(32)` =
`(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