In the given figure, AP is angle bisector of ∠CAE, CP = 7 cm and PE = 8 cm. find the length of AB

In the given figure, AP is angle bisector of ∠CAE, CP = 7 cm and PE = 8 cm. find the length of AB

(a)          32

(b)          25

(c)           49

(d)          56

Sol:

∠BAC = ∠CEA,

In ∆ABC and ∆ABE, AE = 4x, AC = 3.5x

∆ABC ~ ∆ABE

∠B = common.

BC/AB=AC/AE

BC/AB=3.5X/4X

(AB)² = (BC) × (BE)

(4x)² = (3.5x) (3.5x + 15)

16x² = 3.5x (3.5x + 15)

7.5x = 15 × 7

x = 15 × 7/7.5

AB = 4 × 14

= 56 cm