Question

A.What is the length of A’A?
b.What is the length of B’B
Both in units

Answer 1

A'A = 18 units, B'B = 9 units

Explanation:

Δ ACB and Δ A'CB' are similar triangles, thus the ratios of corresponding sides are equal, that is

`(AC)/(A'C)` =
`(AB)/(A'B')` , substitute values

`(AC)/(12)` =
`(20)/(8)` ( cross- multiply )

8AC = 240 ( divide both sides by 8 )

AC = 30

Thus A'A = AC - A'C = 30 - 12 = 18 units

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and

`(CB)/(CB')` =
`(AB)/(A'B')` , that is

`(CB)/(6)` =
`(20)/(8)` ( cross- multiply )

8CB = 120 ( divide both sides by 8 )

CB = 15

Thus

B'B = CB - CB' = 15 - 6 = 9 units