Question

Can someone explain how to do this? Thanks!

Answer 1

Check the picture below.

so we know the quadrilateral is a Rhombus, that means all sides are equal and that the diagonals bisect each other, furthermore the diagonals are perpendicular to each other, what the heck all that means? Well, it means that if we look at any of the triangles, they all have a side of 16 and a hypotenuse of 20, so

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{20}\\ a=adjacent\\ o=\stackrel{opposite}{16} \end{cases} \\\\\\ a=√( 20^2 - 16^2)\implies a=√( 400 - 256 ) \implies a=√( 144 )\implies \stackrel{ EH }{a}=12`

Answer 2

Since DF is 32, you can find FH by dividing that by 2. FH is then 16 and EF is 20. You can now use the Pythagorean theorem by plugging in 16^2 +b^2= 20^2
Which is just 256+ b^2 = 400. So B=the square root of 144. Making EH= 12