Answer:
x = 28
Step-by-step explanation:
ΔARP and ΔCRD are similar. Therefore the sides are in proportion:
[tex]\dfrac{AR}{CR}=\dfrac{PR}{DR}[/tex]
We have:
AR = 10 + x
CR = x
PR = 15 + 42 = 57
DR = 42
Substitute:
[tex]\dfrac{10+x}{x}=\dfrac{57}{42}[/tex] cross multiply
[tex]42(10+x)=57x[/tex] use distributive property
[tex](42)(10)+(42)(x)=57x[/tex]
[tex]420+42x=57x[/tex] subtract 42x from both sides
[tex]420=15x[/tex] divide both sides by 15
[tex]x=28[/tex]
