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Crank
1 year ago
6

HELP HELP HELP HELP HELP HELP HELP HELP HELP

Mathematics
1 answer:
lubasha [3.4K]1 year ago
5 0

{\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 \:  \dfrac{2x}{4}  =  \cfrac{5}{x - 3}

\qquad \sf  \dashrightarrow \:  \dfrac{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

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