Question

In the figure PA=9cm, PB=4cm, and PC is 9 cm more than PD(a) If PD = x find the length of PC ?(b) Find the length of PD ?

Answer 1

Step-by-step explanation:

Given In the figure PA=9 cm, PB=4 cm, and PC is 9 cm more than PD(a) If PD = x find the length of PC ?(b) Find the length of PD ?

• Given PA = 9 cm, PB = 4 cm and PC is 9 cm more than PD. If PD = x we need to find the length of PC and PD.
• Now PD = x
• So PC = x + 9 (According to question)
• Now PC x PD = PA x PB
• Or PC = PA x PB / PD
• So x + 9 = 9 x 4 / x
• So x^2 + 9x = 36
• Or x^2 + 9x – 36 = 0
• Or x^2 + 12x – 3x – 36 = 0
• we get  x(x + 12) – 3(x + 12) = 0
• (x + 12) (x – 3) = 0
• Or x = - 12, 3
• Taking x = 3 we get
• PC = x + 9 = 3 + 9 = 12
• PD = x = 3

Therefore the length of PC = 12 and PD = 3

Reference link will be

https://brainly.in/question/15758085