Answer
(a ) See prove below.
(b)maximum $A=60$ when $x\approx4.6$
Work Step by Step
(a )The crosspieces divide the kite into two isosceles triangles with a common base length of $2x$ and their heights
are given by the Pythagorean formula $h1=\sqrt {5^2-x^2}, h2=\sqrt {12^2-x^2}$. Thus, the total area is given by
$A(x)=\frac{2x}{2}h1+\frac{2x}{2}h2=x(h1+h2)=x(\sqrt {25-x^2}+\sqrt {144-x^2})$
(b) Graph the function above as shown in the figure. A maximum can be found as $A=60$ when $x=4.615\approx4.6$