Answer: " x = 12 " .
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Step-by-step explanation:
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Note: If 2 (two) triangles are "similar" ; then their corresponding sides are "proportional".
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Since one of the sides [the "hypotenuse"] of one the triangles given ; shows the measurement containing an expression with a value of "x" — specifically; " 6x + 28 " ;
→ And since we want to solve for the value of "x" ; we use this "hypotenuse" of said particular triangle to set up a "proportion" with corresponding sides; so we can solve for "x" :
→ Set up proportions as a "ratio" ; or fraction:
→ 7:28::25:(6x + 28) ; Solve for "x" ;
Let us write this in the form of a "fraction" :
→ [tex]\frac{7}{28} = \frac{25}{(6x+28)}[/tex] ;
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Note:
→ Rewrite: " [tex]\frac{7}{28}[/tex] " ; by simplifying to:
" [tex]\frac{1}{4}[/tex] " ;
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→ Since: " [tex]\frac{7}{28}[/tex] " ;
= " (7÷7) / (28÷7) " ;
= " (1 /4) " ;
= " [tex]\frac{1}{4}[/tex] " .
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Now, rewrite the "proportion" ; as follows:
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[tex]\frac{1}{4} = \frac{25}{(6x+28)}[/tex] ;
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Now: "Cross multiply" ; that is:
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→ Given: " [tex]\frac{a}{b} = \frac{c}{d}[/tex] " ;
and: " b[tex]\neq[/tex]0 " ; " d[tex]\neq[/tex]0 " ;
→ Then: " a * d " = " b * c " .
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Likewise: " 1(6x + 28) = (4) * (25) " ;
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SImplify: " 6x + 28 = 100 " ; Solve for "x" ;
→ Subtract "28" from each side of the equation:
→ " 6x + 28 - 28 = 100 - 28 " ;
to get: → " 6x = 72 " ;
Now, divide each side of the equation by: " 6 " ;
to isolate "x" on one side of the equation; & to solve for "x" ; as follows:
→ " 6x = 72 " ;
→ 6x / 6 = 72 / 6 ;
to get:
→ " x = 12 " ;
→ which is the answer.
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Hope this helps!
Best wishes in your academic pursuits
— and within the "Brainly" community!
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