Quadrilateral ABCD is a kite with an area of 80 square inches. The length of BE is 6 inches. What is the length of ED?
To find the length of ED, we first need to determine the height of the kite.
Since ABCD is a kite, we know that the height of the kite is perpendicular to the base (CD) and bisects it. Therefore, the height is the perpendicular distance between CD and the line that contains BE.
Given that the area of the kite is 80 square inches and the length of BE is 6 inches, we can calculate the height using the formula for the area of a kite:
Area = 1/2 * base * height
80 = 1/2 * 6 * height
80 = 3 * height
height = 80 / 3
height ≈ 26.67 inches
Now that we have the height, we can find the length of ED by using the Pythagorean theorem in triangle AED:
ED^2 + AE^2 = AD^2
ED^2 + (height)^2 = (2 * BE)^2
ED^2 + (26.67)^2 = (2 * 6)^2
ED^2 + 712.89 = 144
ED^2 = 144 - 712.89
ED^2 = 567.11
ED ≈ 23.81 inches
Therefore, the length of ED is approximately 23.81 inches.