Question

9. ABCD is a rectangle, sides 36 cm and 90 cm. P is a
point on BC which is one of the longer sides such
that PA = 2PD. The length of PB is?​

Answer 1

Answer:

ANSWER

ABCD is a rectangle.

So, ΔABP & ΔDPC are right ones with PA & PD as hypotenuses .

PA=2PD i.e

PA

2=(2PD)

2 =4PD

2Let PB=x, i.e PC=90−x.

So, applying Pythagoras theorem,

PA 2 =x 2 +36 2⇒4PD

2 =x

2 +36

2

........(i)

PD 2 =(90−x) 2 +36

2⇒4PD

2 =4(90−x)

2 +4×36

2

......(ii)

Comparing (i) & (ii),

x

2 +36

2 =4(90−x)

2+4×36

2⇒37584−720x+36288=0

⇒(x−168)(x−72)=0

⇒x=(168,72)cm.

We reject x=PB=168 as PB is the part of BC=90cm.

∴x=PB=72cm.

solution