Answer:
Total amount needed is: $59.25
Step-by-step 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:
[tex]17 ^ 2 = h ^ 2 + 8 ^ 2[/tex] --- Pythagoras theorem
[tex]289 = h^2 + 64[/tex]
Collect like terms
[tex]h ^ 2 = 289 - 64[/tex]
[tex]h ^ 2 = 225[/tex]
Take positive square root of both sides
[tex]h = \sqrt{225[/tex]
[tex]h = 15[/tex]
Next, calculate the area of the fence (trapezium).
This is calculated as:
[tex]Area = \frac{1}{2}(a + b) * h[/tex]
Where:
[tex]a = 12[/tex]
[tex]b = 20 + 8 = 28[/tex]
So, we have:
[tex]Area = \frac{1}{2}(12 + 28) * 15[/tex]
[tex]Area = \frac{1}{2}(40) * 15[/tex]
[tex]Area = 20 * 15[/tex]
[tex]Area = 300m^2[/tex]
From the question, we have:
[tex]\$19.75 = 100m^2[/tex]
Let x = the cost required for the complete area
i.e.
[tex]x = 300m^2[/tex]
So, we have:
[tex]\$19.75 = 100m^2[/tex]
[tex]x = 300m^2[/tex]
Cross multiply
[tex]x * 100m^2 = \$19.75 * 300m^2[/tex]
Divide both sides by [tex]100m^2[/tex]
[tex]\frac{x * 100m^2}{100m^2} = \frac{\$19.75 * 300m^2}{100m^2}[/tex]
[tex]x = \frac{\$19.75 * 300m^2}{100m^2}[/tex]
[tex]x = \$19.75 * 3[/tex]
[tex]x = \$59.25[/tex]
