Final answer:
To find the length of the diagonals of a kite, we can use the Pythagorean theorem. Given the lengths of the two diagonals, we can substitute them into the equation and solve for the hypotenuse.
Step-by-step explanation:
To determine the length of the diagonals of a kite, we can use the Pythagorean theorem. Let's label the length of the first diagonal as 'd1' and the length of the second diagonal as 'd2'. We can then use the formula d1^2 + d2^2 = c^2, where 'c' represents the length of the hypotenuse (the length between the endpoints of the diagonals).
Given that d1 = 19.87 cm and d2 = 15.32 cm, we can substitute these values into the equation and solve for 'c'. Plugging in the values, we get:
19.87^2 + 15.32^2 = c^2
Simplifying the equation, we have:
394.2169 + 235.4624 = c^2
629.6793 = c^2
Taking the square root of both sides, we find that c = 25.09 cm (rounded to the nearest 1/100 cm).