Question

Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?

Answer 1

Complete Question:

Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters.  This year he wants to make the garden three times as long and two times as wide.  

Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.  

How many more meters of fencing is needed for this year’s garden than last year’s?

Answer:

26 meters of fencing needed

Step-by-step explanation:

Given

Last Year:

$Width = 5m$

$Area = 20m^2$

This Year:

$Length = 3\ times\ longer$

$Width = 2\ times\ wider$

Required

Determine how many more meters is needed

Represent last year's length of Fence with L and last year's width with W

First, we need to calculate L

$Area = L * W$

Where

$Area = 20m^2$

$W = 5m$

$20m^2 = L * 5m$

Divide both sides by 5m

$\frac{20m^2}{5m} = \frac{L * 5m}{5m}$

$\frac{20m^2}{5m} = L$

$L = \frac{20m^2}{5m}$

$L = 4m$

So, we have that:

For Last Year

$Length = 4m$ and $Width = 5m$

For this year:

$Length = 3\ times\ longer$

$Length = 3 * 4m$

$Length = 12m$

$Width = 2\ times\ wider$

$Width = 2 * 5m$

$Width = 10m$

So, for this year, we have:

$Length = 12m$ and $Width = 10m$

Next, we calculate perimeter of fencing in both years.

$Perimeter = 2 * (Length + Width)$

Last Year:

$Perimeter = 2 * (4m + 5m)$

$Perimeter = 2 * 9m$

$Perimeter = 18m$

This Year:

$Perimeter = 2 * (12m + 10m)$

$Perimeter = 2 * 22m$

$Perimeter = 44m$

To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.

$Difference = 44m - 18m$

$Difference = 26m$

Hence, there are 26 meters of fencing needed