Can somebody please help me quick?

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Can somebody please help me quick?

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Answer 1 · 2018-05-18T21:10:34

$x = - \frac{3}{2} \to (B)$ $x=-3/2to(B)$

Explanation:

$since the triangles are similar then the ratios of$ $"since the triangles are similar then the ratios of "$
$corresponding sides are equal$ $"corresponding sides are equal"$

$\Rightarrow \frac{A B}{X Y} = \frac{A C}{X Z} = \frac{C B}{Z Y}$ $rArr(AB)/(XY)=(AC)/(XZ)=(CB)/(ZY)$

$using \frac{A C}{X Z} = \frac{C B}{Z Y}$ $"using "(AC)/(XZ)=(CB)/(ZY)$

$\Rightarrow \frac{x + 6}{3 - x} = \frac{x + 7}{4 - x} \leftarrow cross-multiply$ $rArr(x+6)/(3-x)=(x+7)/(4-x)larrcolor(blue)"cross-multiply"$

$(x + 6) (4 - x) = (x + 7) (3 - x) \leftarrow distribute$ $(x+6)(4-x)=(x+7)(3-x)larrcolor(blue)"distribute"$

$4x+24cancel(-x^2)-6x=3x+21cancel(-x^2)-7x$

$rArr-2x+24=-4x+21$

$"add "4x " to both sides"$

$rArr2x+24=21$

$"subtract 24 from both sides"$

$rArr2x=-3$

$"divide both sides by 2"$

$rArrx=-3/2to(B)$

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