Answer:
2.4 cans cost 47.4
If you cannot buy 2.4 cans, you must buy 3 cans, then you'll pay 59.25
Step-by-step explanation:
The lawn has trapezoidal shape, so find the area of the trapezoid using formula
[tex]A=\text{Midline}\times \text{Height}[/tex]
In the diagram, ABED is rectangle, so BE = 12 m, thus ED = 20 m - 12 m = 8 m.
Consider right triangle EDC. By the Pythagorean theorem,
[tex]ED^2+EC^2=CD^2\\ \\ED^2+8^2=17^2\\ \\ED^2=289-64\\ \\ED^2=225\\ \\ED=15\ m[/tex]
Thue,
Height = 15 m
Find the midline:
[tex]\text{Midline}=\dfrac{AD+BC}{2}=\dfrac{12+20}{2}=16\ m[/tex]
Hence,
[tex]A=16\cdot 15=240\ m^2[/tex]
One can cover [tex]100\ m^2,[/tex] to cover [tex]240\ m^2[/tex] is needed
[tex]240:100=2.4[/tex] cans
One can costs 19.75, so 2.4 cans cost
[tex]19.75\cdot 2.4=47.4[/tex]
If you cannot buy 2.4 cans, you must buy 3 cans, then you'll pay
[tex]19.75\cdot 3=59.25[/tex]
