Answer:
The value of x in centimeters is 22.5 cm
Step-by-step explanation:
The corresponding sides of the similar triangles are proportion which means have equal ratios
∵ Δ ABC is similar to Δ FGH
∵ AB and FG are corresponding sides
∵ BC and GH are corresponding sides
∵ AC and FH are corresponding sides
→ That means the ratios between them are equal
∴ [tex]\frac{AB}{FG}[/tex] = [tex]\frac{BC}{GH}[/tex] = [tex]\frac{AC}{FH}[/tex]
∵ AB = 6 cm and FG = 15 cm
∵ BC = 5 cm and GH = 12.5 cm
∵ AC = 9 cm and FH = x
→ Substitute them in the rule above to find x
∴ [tex]\frac{6}{15}[/tex] = [tex]\frac{5}{12.5}[/tex] = [tex]\frac{9}{x}[/tex]
→ By using cross multiplication with the 1st and 3rd ratios
∵ 6 × x = 15 × 9
∴ 6x = 135
→ Divide both sides by 6 to find x
∵ [tex]\frac{6x}{6}[/tex] = [tex]\frac{135}{6}[/tex]
∴ x = 22.5 cm
∴ The value of x in centimeters is 22.5 cm
