The diagonals are:
diagonal₁=2x+3y
diagonal₂=(x+8)+(2y+5)
We have to solve the following system of equations:
2x=3y
(x+8)=(2y+5)
We solve this system by substitution method:
2x=3y ⇒x=3y/2
(3y/2 +8)=2y+5
3y+16=4y+10
-y=-6
y=6
x=3y/2=3*6/2=9
we obtain the measure of the diagonals:
diagonal₁=2x+3y=2*9+3*6=18+18=36
diagonal₂=(x+8)+(2y+5)=(9+8)+(2*6+5)=17+17=34
Answer: The longest diagonal is 36 units.
