Question

Calculate AD and hence BD.

Answer 1

Answer:

AD = 15 cm , BD = 3 cm

Step-by-step explanation:

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

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

$\frac{AD}{AB}$ = $\frac{DE}{BC}$ ( substitute values )

$\frac{AD}{12}$ = $\frac{10}{8}$ ( 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