Question

(HELP ASAP) 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

The answer is 5 units on e2020.

Answer 2

Let's say that FH and EG intersection is O,
So we have the following:
OF = 2
OH = 5

Just because F and H are midpoints it means that EO = OG = x
And as it's given the area S=35

On the other hand
S = OF*OG/2 + OG*OH/2 + OH*OE/2 + OE*OF/2 = 2*x/2 + x*5/2 + 5*x/2 + x*2/2 = 2*x + 5*x = 7*x = 35

7x = 35 so x = 35/7 = 5

Answer: 5 units