Question

What is the value of x?

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units

Answer 1

AP and CD are parallel. Therefore the segments AC, CR, DR and PD are in proportion:

`(CR)/(DR)=(AC)/(PD)`

We have

CR = x

DR = 42

AC = 10

PD = 15

Substitute:

`(x)/(42)=(10)/(15)` cross multiply

`15x=(42)(10)`

`15x=420` divide both sides by 15

`x=(420)/(15)`

`\boxed{x=28}`

Answer 2

x = 28

Explanation:

We have similar triangles so

RC RD

----------- = -------------

RA RP

Substituting in

x 42

----------- = -------------

x+10 42+15

x 42

----------- = -------------

x+10 57

Using cross products

57*x = 42(x+10)

Distribute

57x = 42x+420

Subtract 42 from each side

57x-42x = 42x-42x+420

15x = 420

Divide by 15

15x/15 = 420/15

x = 28