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

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:

$17 ^ 2 = h ^ 2 + 8 ^ 2$ --- 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:

$Area = \frac{1}{2}(a + b) * h$

Where:

$a = 12$

$b = 20 + 8 = 28$

So, we have:

$Area = \frac{1}{2}(12 + 28) * 15$

$Area = \frac{1}{2}(40) * 15$

$Area = 20 * 15$

$Area = 300m^2$

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 $100m^2$

$\frac{x * 100m^2}{100m^2} = \frac{\ 19.75 * 300m^2}{100m^2}$

$x = \frac{\ 19.75 * 300m^2}{100m^2}$

$x = \ 19.75 * 3$

$x = \ 59.25$