Question

Calculate AD and hence BD.

Answer 1

AD = 15 cm , BD = 3 cm

Explanation:

Δ ABC is similar to Δ ADE ( by the AA postulate )

then the ratios of corresponding sides are in proportion, that is

`(AD)/(AB)` =
`(DE)/(BC)` ( substitute values )

`(AD)/(12)` =
`(10)/(8)` ( cross- multiply )

8 × AD = 12 × 10 = 120 ( divide both sides by 8 )

AD = 15 cm

AB + BD = AD , that is

12 + BD = 15 ( subtract 12 from both sides )

BD = 3 cm