Question

1. In this diagram, the area of the small square is 1/9 of the area of the large
square. Find x/y

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Answer 1

Answer:

$area \: of \: small \: square \: = x \times x = {x}^{2} \\ area \: of \: larger \: square \\ = (x + y)(x + y) = {(x + y)}^{2} \\ according \: to \: question \\ {x}^{2} = \frac{1}{9} \times (x + y) {}^{2} \\ 9 {x}^{2} = {(x + y)}^{2} \\ {(3x)}^{2} = {(x + y)}^{2} \\ {(x + y)}^{2} - {(3x)}^{2} = 0 \\ (x + y - 3x)(x + y + 3x) = 0 \\ (y - 2x)(y + 4x) = 0 \\ so \\ y = 2x \: or \: - 4x \\ then \\ \frac{x}{y} = \: \frac{x}{2x} = \frac{1}{2} \\or \\ = \frac{x}{ - 4x} = - \frac{1}{4} \\ {.}^{.} . \: \frac{x}{y} = \frac{1}{2} \: or \: - \frac{1}{4}$

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