Question

12 m Fence 17 m 20 m one can of weedkiller can cover 100 square metres. eachh can costs $19.75 work out the total cost of the cans of weedkiller needed to cover the lawn.

Answer 1

Total amount needed is: $59.25

Explanation:

Given

See attachment for fence

Required

Cost of weedkiller needed

First, we need to calculate the height of the fence.

Considering the triangular end of the fence, we have:

`17 ^ 2 = h ^ 2 + 8 ^ 2` --- Pythagoras theorem

`289 = h^2 + 64`

Collect like terms

`h ^ 2 = 289 - 64`

`h ^ 2 = 225`

Take positive square root of both sides

`h = \sqrt{225`

`h = 15`

Next, calculate the area of the fence (trapezium).

This is calculated as:

`Area = (1)/(2)(a + b) * h`

Where:

`a = 12`

`b = 20 + 8 = 28`

So, we have:

`Area = (1)/(2)(12 + 28) * 15`

`Area = (1)/(2)(40) * 15`

`Area = 20 * 15`

`Area = 300m^2`

From the question, we have:

`\$19.75 = 100m^2`

Let x = the cost required for the complete area

i.e.

`x = 300m^2`

So, we have:

`\$19.75 = 100m^2`

`x = 300m^2`

Cross multiply

`x * 100m^2 = \$19.75 * 300m^2`

Divide both sides by
`100m^2`

`(x * 100m^2)/(100m^2) = (\$19.75 * 300m^2)/(100m^2)`

`x = (\$19.75 * 300m^2)/(100m^2)`

`x = \$19.75 * 3`

`x = \$59.25`