Question

What is the value of x? Enter your answer in the box. ___ units

Answer 1

x = 28

Explanation:

Consider the two triangles ΔAPR and ΔCDR

We see that AP ║ CD

Therefore m∠PAR = m∠CR, m∠APR= m∠CDR
Angle ∠R is common to both triangles

So the triangles are similar

Therefore the ratios of the sides must be the same ratio

`(AR)/(CR) = (PR)/(DR)\\\\`

AR = x + 10

CR = x

PR = 42 + 15 = 57

DR = 42

PR = 42 + 15 = 57

Plugging in the values for these sides:

`(x + 10)/(x) = (57)/(42)\\`

Cross-multiplying we get

`42(x + 10) = 57x\\\\42x + 420 = 57x\\\\420 = 57x - 42x = 15x\\\\15x = 420\\\\x = 420/15\\\\= 28`