Question

Please help me if you are thankful for everything here is the picture

Answer 1

The value of x in centimeters is 22.5 cm

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

∴
`(AB)/(FG)` =
`(BC)/(GH)` =
`(AC)/(FH)`

∵ 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

∴
`(6)/(15)` =
`(5)/(12.5)` =
`(9)/(x)`

→ By using cross multiplication with the 1st and 3rd ratios

∵ 6 × x = 15 × 9

∴ 6x = 135

→ Divide both sides by 6 to find x

∵
`(6x)/(6)` =
`(135)/(6)`

∴ x = 22.5 cm

∴ The value of x in centimeters is 22.5 cm