Verified Answer :

JonHenderson55

Answer:   y = 6 mi.  .
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Explanation:
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Area of a triangle = (½) (base) (height) ;

or,  A = (½) b h ;  or,  A = bh / 2 ;
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Given:  A = 24.3 mi ² ;
           b = 8.1 mi 
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Find the height, "h" ;  (in units of "miles", or , "mi" ).
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   Plug in the known values into the formula:

24.3 mi ² = (½) (8.1 mi) (h) ;
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Solve for "h" (height) ;
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(½) (8.1 mi) = 4.05 mi  ;
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Rewrite: 
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24.3 mi² = (4.05 mi) (h) ;  Solve for "h" ;
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 Divide each side of the equation by "(4.05 mi)" ; to isolate "h" on one side of the equation ; and to solve for "h" ; 
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   24.3 mi²  / 4.05 mi  = (4.05 mi) (h)  / 4.05 mi ;
                                 
              →  6 mi  = h ;  ↔  h = 6 mi. 

              →      h = y = 6 mi. 
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altavistard

I'd suggest you begin with the formula for the area of a triangle of base b and height h.  It is as follows:

         bh
A = --------
          2

Here b is the length of the base and h is the height of the triangle.
In this problem the area and the base are given; they are 24.3 square miles and 8.1 miles respectively. We are to determine the height, y.

                                                                                          2A  
Solve the above equation for h, the height:  2A=bh, or  -------
                                                                                            b

Substitute (24.3 square miles) for A and 8.1 miles for b.

Calculate y (or, equivalently, calculate h).  Both represent the height of the given triangle.

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