Question

Suppose BK is an angle bisector of △ABC. Find AB if BC=5, and AK=2.625, and KC=4.375.

Answer 1

Answer:

AB=3

Step-by-step explanation:

Given: AB=x, BC=5 AK=2.625, and KC=4.375

AB/BC=AK/KC

Because AK is similar to KC, and BA is similar to BC.

Triangle ABK and Triangle CBK are similar since they have an angle bisector.

so :

x/5=2.625/4.375

4.275x=2.625(5)

4.275x=13.125

x=13.125/4.275

x=3

AB=3

Answer 2

Answer:

AB = 3

Step-by-step explanation:

given that BK is an angle bisector then the following ratios are equal

$\frac{AB}{BC}$ = $\frac{AK}{KC}$

substitute relevant values into the equation and solve for AB

$\frac{AB}{5}$ = $\frac{2.625}{4.375}$ ( cross- multiply )

4.375AB = 13.125 ( divide both sides by 4.375 )

AB = 3