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HELP HELP HELP
HELP HELP HELP
HELP HELP HELP

HELP HELP HELP HELP HELP HELP HELP HELP HELP-example-1
User Guice
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{\qquad\qquad\huge\underline{{\sf Answer}}}

As per the given information ~

The given triangles are similar, so their corresponding sides should be in same ratio :


\qquad \sf  \dashrightarrow \: (2x)/(4) = \cfrac{5}{x - 3}


\qquad \sf  \dashrightarrow \: (x)/(2) = \cfrac{5}{x - 3}


\qquad \sf  \dashrightarrow \: x(x - 3) = 10


\qquad \sf  \dashrightarrow \: {x}^(2) - 3x = 10


\qquad \sf  \dashrightarrow \: {x}^(2) - 3x - 10 = 0


\qquad \sf  \dashrightarrow \: {x}^(2) - 5x + 2x - 10 = 0


\qquad \sf  \dashrightarrow \: x(x - 5) + 2(x - 5) = 0


\qquad \sf  \dashrightarrow \: (x + 2)(x - 5) = 0

so, x = 5 or -2

but since side length can't be negative, we will take x = 5 neglecting the negative value (-2)

So, side lengths of unknown sides are :


\qquad \sf  \dashrightarrow \: {2x = 2 × 5 = 10 units}

and


\qquad \sf  \dashrightarrow \: x - 3 = 5 - 3 = 2 \: \: units

User MillerC
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