Question 1150800



We can equate the area as follows

 

{{{A=(1/2)base * height =  65 *  height }}}...      (1)  

{{{A=120 * (1/2)side  =  60 * side}}}..........    (2)

 

Set (1)  = (2)      and solve for the side

 

{{{60 * side  =  65 * height}}}

 

{{{side  = (65/60) * height}}}

 

{{{side  =  (13/12)* height  =   (13/12)*h}}}

 

The side  is the {{{hypotenuse }}}of a right triangle with the height and {{{1/2 }}}base being the legs

 

So, using the Pythagorean Theorem, we have that

 

{{{sqrt  ( side^2  -  height^2 )  =  (1/2)* base}}}}

 

Substitute

 

{{{sqrt  ( ( (13/12)h)^2  - h^2)  =  (1/2)* base }}}       

 

{{{sqrt  ((169/ 144)h^2 -  (144/144)h^2)  = (1/2)* base }}}  



 {{{sqrt ( (169 - 144) h^2    / 144 )   =  (1/2 )*base}}}

 

{{{sqrt ( 25h^2 / 144 ) =  (1/2)* base}}}

 

{{{(h / 12) * sqrt (25)  =  (1/2)* base}}}

 

{{{(5/12)h  =  (1/2 )130}}}

 

{{{(5/12)h  =  65}}}

 

{{{h = (65*12) / 5 }}} 

 

{{{h  = 13 * 12  =   156 m}}}

 

So,

{{{Area  = (1/2)base * height}}}

 

{{{Area  =(1/2)130m * 156m}}}

 

{{{Area  =65m * 156m  }}} 

 

{{{Area  =10140 m^2}}}