Question

fghj is a kite. find gh. leave your answer as a simplified radical.

Explanation:

Step1: Identify right triangle for GH

The diagonals of a kite are perpendicular, so the segment GH is the hypotenuse of a right triangle with legs 4 and 6.

Step2: Apply Pythagorean theorem

Use $c=\sqrt{a^2+b^2}$ where $a=4$, $b=6$.
$$GH=\sqrt{4^2+6^2}$$

Step3: Simplify the radical

Calculate the value inside the square root, then factor out perfect squares.
$$GH=\sqrt{16+36}=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$$

Answer:

$2\sqrt{13}$