Sofia cuts a piece of felt in the shape of a kite for an art project. the top two sides measure 20 cm each and the bottom two sides measure 13 cm each. one diagonal, eg, measures 24 cm. what is the length of the other diagonal, df? 5 cm 16 cm 21 cm 32 cm

x + y  = 24       where x and y are the 2 parts of diagonal Other diagonal wil be smaller that 24. 
x^2 + z^2 = 13^2
y^2 + z^2  = 20^2            where z  = 0.5 * length of smaller diagonal)

form last 2 equations

y^2 - x^2  = 20^2 - 13^2  =  231
 now y = 24-x so we have

(24 - x)^2    - x^2 = 231

576 - 48x = 231

48x = 345

x =  7.1875

z^2  =  13^2 - 7.1875^2 =  117.34
z =  1.83

so smaller diagonal = 21.66 cm

looks like its the third choice.

What’s the improper fraction?

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2