The trapezoid HJKL has T and S as midpoints of the legs
The length of TS can be calculated as the mean or average of the lengths of HJ and LK, i.e.:
[tex]TS=\frac{HJ+LK}{2}[/tex]
We are given the lengths HJ=14, LK=42, thus:
[tex]TS=\frac{14+42}{2}=\frac{56}{2}=28[/tex]
Now if we have HJ=7 and TS=10, we can find LK by solving the equation for LK
[tex]LK=2TS-HJ[/tex][tex]LK=2*10-7=20-7=13[/tex]
The length of LK is 13
