Question

Please help me with this one question, and I'll upvote the brainliest answer

Answer 1

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" :

      →  $\frac{7}{28} = \frac{25}{(6x+28)}$ ;

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Note:  

        →  Rewrite:  " $\frac{7}{28}$ " ; by simplifying to:

                                    " $\frac{1}{4}$ " ;

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         →  Since:  " $\frac{7}{28}$ " ;

              =  " (7÷7) / (28÷7) " ;

              =  " (1 /4) " ;

              =   " $\frac{1}{4}$ " .

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Now, rewrite the "proportion" ; as follows:

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        $\frac{1}{4} = \frac{25}{(6x+28)}$  ;

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Now:   "Cross multiply" ;  that is:

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→   Given:   " $\frac{a}{b} = \frac{c}{d}$ " ;  

         and:  " b$\neq$0 " ;  " d$\neq$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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