Question

Solve for x. The triangles in each pair are similar.

Answer 1

x = 8 and x = 9

Explanation:

given the triangles are similar , then the ratios of corresponding sides are in proportion

17

`(SR)/(CB)` =
`(ST)/(CD)` ( substitute values )

`(11x-4)/(60)` =
`(70)/(50)` ( cross- multiply )

50(11x - 4) = 60 × 70 = 4200 ( divide both sides by 50 )

11x - 4 = 84 ( add 4 to both sides )

11x = 88 ( divide both sides by 11 )

x = 8

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18

`(BC)/(ED)` =
`(AB)/(FE)` ( substitute values )

`(11x+11)/(30)` =
`(77)/(21)` ( cross- multiply )

21(11x + 11) = 30 × 77 = 2310 ( divide both sides by 21 )

11x + 11 = 110 ( subtract 11 from both sides )

11x = 99 ( divide both sides by 11 )

x = 9