The diagram shows the shape of a plot of land that maria will use for her garden.

she needs to know the length of each side so she can buy fencing. what is the length of line segment fj?

18 feet
30 feet
36 feet
42 feet

K so we're gonna take this in sections. The triangle is going to be sectioned off so that the two sides with 24 ft are made into a square. we need to find the remaining bit of the side that makes up the triangle. Fortunately, I know right triangles. So we use the Pythagorean theorem. 

a^2 + b^2 =c^2, with c being the hypotenuse, or the long/slanted side. so we have
576 +b^2=900, because a and b are interchangeable, and the other side we know is the same as the side of the square. 

900-576 = b^2 I just flipped it. 
324=b^2
and now we have to find the square root of 324. Go, calculator!
our remaining side is 18. I checked, and 18*18 does equal 324.
SO we add 18+24 to get our longest side, FJ. FJ turns out to be 42. 

The answer is 42. (THE ANSWER TO THE UNIVERSE)