Question

In 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.

Answer 1

Given

∠A = ∠C,

AB = 6 cm, BP = 15 cm,

AP = 12 cm

CP = 4 cm

From ∆APB and ∆CPD,

∠A = ∠C

∠APB = ∠CPD  .....[Vertically opposite angles]

∴ By AAA similarity criteria,

ΔAPD ∼ ΔCPD

Using basic proportionality theorem,

⇒ `(AP)/(CP) = (PB)/(PD) = (AB)/(CD)`  ......[By basic proportionality theorem]

⇒ `12/4 = 15/(PD) = 6/(CD)`

Considering `(AP)/(CP) = (PB)/(PD)`, we get,

`12/4 = 15/(PD)`

`PD = (15 xx 4)/12 = 60/12` = 5 cm

Considering, `(AP)/(CP) = (AB)/(CD)`

⇒ `CD = ((6 xx 4))/12` = 2 cm

Therefore,

Length of PD = 5 cm

Length of CD = 2 cm