1 Answer

MillerC · Answer 1 · 2023-09-12T01:25:51+0000

${\qquad\qquad\huge\underline{{\sf Answer}}}$

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

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

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