Question

Alright, second try. 15 Points to whoever can solve with a half-decent explanation.

Answer 1

29 cans

Explanation:

To solve this problem we must use Heron's formula; A =
`√(S(S-a)(S-b)(S-c))`

S = 1/2 the perimeter of the given triangle

a, b, c = the measurements of the three given sides

The first step to solving this question is first finding the perimeter.

P = 65m + 74m + 67m

P = 206m

Now that we have our perimeter, we must divide P by 2 to get S.

S = 206/2

S = 103

Now we plug our numbers into Heron's formula.

A =
`√(S(S-a)(S-b)(S-c))`

A =
`√(103(103-65)(103-67)(103-74))`

A =
`√(103(38)(36)(29))`

A =
`√(103(39672))`

A =
`√(4086216)`

Find the square root of this number.

A ≈ 2021.43909134... m²

If a can of paint covers 70 square meters, then you will need to figure out how many cans you need. This can be done by dividing the overall area of the triangle by the area that a single can of paint can cover.

`(2021.43909134...)/(70)` = 28.8777013049...

We know we can't buy 28.87... of a can (people simply do not sell parts of cans or half-full containers... unless its a bag of lays chips and their 80% air nonsense...) so we must round up to the nearest whole number.

28.87... = 29

Thus we finally have our answer: 29 cans of paint!