In given figure, if ∠ A = ∠ C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then find the lengths of PD and CD.

Question

Philoid · Accepted Answer

Given,

∠A = ∠C,

AB = 6 cm, BP = 15 cm,

AP = 12 cm

CP = 4 cm

In ∆APB and ∆CPD,

∠A = ∠C [given]

∠APB = ∠CPD [vertically opposite angles]

∴ By AAA similarity criteria,

∆APD ∼ ∆CPD

By taking first two terms,

By taking first and last terms,

Hence,

length of PD = 5 cm

length of CD = 2 cm