Answer:
x = 7
Step-by-step explanation:
Given that ∆BCD ~ ∆BFG, therefore the ratio of their corresponding side lengths will be equal.
Thus:
[tex] \frac{BC}{BF} = \frac{BD}{BG} [/tex]
Substitute
[tex] \frac{17x + 13}{36} = \frac{154}{42} [/tex]
Cross multiply
[tex] 42(17x + 13) = 154(36) [/tex]
[tex] 714x + 546 = 5,544 [/tex]
[tex] 714x = 5,544 - 546 [/tex] (subtraction property of equality)
[tex] 714x = 4,998 [/tex]
Divide both sides by 714
x = 7
