Question

PLEASE HELP ME!! 1.02: Triangle Similarity 1 What is the value of X?

Answer 1

Answer:

x = 28

Step-by-step explanation:

ΔARP and ΔCRD are similar. Therefore the sides are in proportion:

$\dfrac{AR}{CR}=\dfrac{PR}{DR}$

We have:

AR = 10 + x

CR = x

PR = 15 + 42 = 57

DR = 42

Substitute:

$\dfrac{10+x}{x}=\dfrac{57}{42}$           cross multiply

$42(10+x)=57x$             use distributive property

$(42)(10)+(42)(x)=57x$

$420+42x=57x$         subtract 42x from both sides

$420=15x$            divide both sides by 15

$x=28$