Question 83091
We know that the area of any triangle ]is given by :  


A = {{{(1/2) * b * h }}}  Where A = Area, b = base of the triangle, h = height of the triangle



According to the given data, Area =  12 sq ft, height = 48 ft 



so, substituting in the formula, we get:  


12 = {{{(1/2)* b * 48 }}} 


==>  12 =  b * 24 


==> {{{(12/24) = b }}} 


==> {{{(1/2) = b}}} 


==> Therfore, the width of the bottom is 1/2 " 


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Given area = 12 sq ft  and the width of the bottom is 6 ft, to find the height of the triangle 


Area = {{{(1/2)}}} * b * h  


Substituting for the values, we get: 


12 =  {{{(1/2)}}} * 6 * h 


==> 12 =  3 * h 


==> {{{12/3}}} = h 


==>  4 = h 


Hence, the height of the opening is 4 ft. 



Thus, the solution.. 


HAPPY CALCULATING!!