Question

Can somebody help me with the Math's questions on Pythagoras Theorem? Thanks

Answer 1

2.4 cans cost 47.4

If you cannot buy 2.4 cans, you must buy 3 cans, then you'll pay 59.25

Explanation:

The lawn has trapezoidal shape, so find the area of the trapezoid using formula

`A=\text{Midline}* \text{Height}`

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,

`ED^2+EC^2=CD^2\\ \\ED^2+8^2=17^2\\ \\ED^2=289-64\\ \\ED^2=225\\ \\ED=15\ m`

Thue,

Height = 15 m

Find the midline:

`\text{Midline}=(AD+BC)/(2)=(12+20)/(2)=16\ m`

Hence,

`A=16\cdot 15=240\ m^2`

One can cover
`100\ m^2,` to cover
`240\ m^2` is needed

`240:100=2.4` cans

One can costs 19.75, so 2.4 cans cost

`19.75\cdot 2.4=47.4`

If you cannot buy 2.4 cans, you must buy 3 cans, then you'll pay

`19.75\cdot 3=59.25`