Question

Kite E F G H is inscribed in a rectangle. Points F and H are midpoints of sides of the rectangle, and creates a side length of x. Lines are drawn from point F to point H and from point E to point G and intersect at a point. Line E G is parallel to a rectangle side. The distance from point F to the intersection is 2, and the distance from H to the intersection is 5.
Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides.

The area of EFGH is 35 square units. What is the value of x?

4 units
5 units
6 units
7 units

Answer 1

7 units

Reason: F and H are midpoints of opposite sides, so FH is the kite's diagonal of length x. The intersection divides FH into segments 2 and 5, so x = 2 + 5 = 7.