Question 1157986

<a href="https://www.imageupload.net/image/D7aot"><img src="https://imagehost.imageupload.net/2020/05/04/kite.th.png" alt="kite.png" border="0" /></a>



In order to solve this problem, first observe that the red diagonal line divides the kite into two triangles that each have side lengths of {{{15}}} and {{{8}}}. Notice, the hypotenuse of the interior triangle is the red diagonal. Therefore, use the Pythagorean theorem: 

{{{a^2+b^2=c^2}}}, where {{{c}}}= the length of the red diagonal. 

The solution is: 

{{{8^2+15^2=c^2}}}

{{{64+225=c^2}}}

{{{c^2=289}}}

{{{c=sqrt(289)}}}

{{{c=17in }}}

 
the other diagonal {{{d}}}:

recall that the area of a kite is half the product of the diagonals 

{{{A=c*d/2}}}....since {{{c=17}}}

{{{A=17*d/2}}}...eq.1

The diagonals of the kite are the height and width of the {{{rectangle}}} it is superimposed in, and we know that because the area of a rectangle is base times height.

Therefore the area of a rectangle is:

{{{A=15*8=15*4=120}}}


substitute in the area of a kite:

{{{120=17*d/2}}}

{{{240=17d}}}

{{{d=240/17}}}

{{{d=14.118in}}}