Question

A garden measuring 15 meters by 20 meters is to have a pedestrian pathway installed
all around it, increasing the area to 336 square meters.
a. Write an expression to represent the area of the total garden including the
pathway.

b. What will be the width of the pathway?

Answer 1

The area of the garden is the amount of space on the garden.

• The area of the total garden is (x + 15)(x + 20)
• The width of the pathway is 1 meter

The expression of the area

The dimensions of the garden is given as:

15 meters by 20 meters

Let the width of the pedestrian pathway be x.

So, the area of the total garden is:

$Area=(x + 15)(x + 20)$

The width of the pathway

In (a), we have:

$Area=(x + 15)(x + 20)$

The total area is given as: 336.

So, we have:

$(x + 15)(x + 20) = 336$

Expand

$x^2 + 35x + 300 = 336$

Collect like terms

$x^2 + 35x + 300 - 336 = 0$

Evaluate

$x^2 + 35x - 36 = 0$

Expand

$x^2 + 36x -x - 36 = 0$

Factorize

$x(x + 36) -1(x +36) = 0$

Factor out x + 36

$(x + 36)(x -1) = 0$

Solve for x

x = -36 or x =1

The width cannot be negative.

Hence, the width of the pathway is 1 meter

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