Question

Quadrilaterals ABCD and PQRS shown below are two similar figures.
Find the values of x and y.​

Answer 1

x = 12, y = 16

Explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

`(AD)/(PS)` =
`(DC)/(SR)` , substitute values

`(20)/(2x+6)` =
`(18)/(27)` ( cross- multiply )

18(2x + 6) = 540 ( divide both sides by 18 )

2x + 6 = 30 ( subtract 6 from both sides )

2x = 24 ( divide both sides by 2 )

x = 12

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and

`(AB)/(PQ)` =
`(DC)/(SR)` , substitute values

`(y)/(24)` =
`(18)/(27)` ( cross- multiply )

27y = 432 ( divide both sides by 27 )

y = 16