Answer:
We can use the formula for the area of a kite, which is (1/2) x (diagonal1) x (diagonal2), to solve this problem.
Let's assume that the two diagonals of the kite have lengths d1 and d2, with d1 being the longer diagonal. We know that the area of the kite is 28 m^2, so we have:
(1/2) x d1 x d2 = 28
We also know that the height of the kite is 4 m, and the length of the other diagonal is 10 m. The height of the kite partitions the longer diagonal into two segments, each with length x. By the Pythagorean theorem, we have:
x^2 + 4^2 = (d2/2)^2
Simplifying, we get:
x^2 + 16 = (d2^2)/4
Multiplying both sides by 4, we get:
4x^2 + 64 = d2^2
Substituting d2 = 10, we have:
4x^2 + 64 = 100
Solving for x, we get:
4x^2 = 36
x^2 = 9
x = 3
Therefore, the value of x (the length of one of the two segments of the longer diagonal that are partitioned by the height) is 3 meters.
Explanation: