The lengths of a rectangular garden, the inner rectangle, is 9ft more than its width. For the garden. Let x = width, x + 9 = length. It is surrounded by a brick walkway 4ft wide. Suppose the total area of the walkway is 400ft^2. a. Write a polynomial to represent the length of PQ

b. What are the dimensions of the garden?

The dimension of the garden is 52.5ft by 43.5ft

Step-by-step explanation:

Given

The shape above

Required

Determine PQ

Determine dimension of the garden

Calculating Length PQ

Represent the length of the inner rectangle as L

Represent the width of the inner rectangle as W

The distance between the inner rectangle and the outer triangle is 4ft

This implies that;

Substitute for

Also;

Substitute for

Calculating The Dimension of The Garden

First, we need to determine the Area of the inner rectangle

Recall that   and

So;

For the bigger rectangle

Recall that   and

So;

Given that the Area of the walkway is

This implies that

Substitute and

Open All Brackets

Collect Like Terms

Divide both sides by 8

Since the dimensions of the garden is and

Substitute 43.5 for x in both cases

Hence, the dimension of the garden is 52.5ft by 43.5ft

perimeter = 10 +  √10  units

explanation:

first, we will need to get the length of each line using the distance formula which is as follows:

distance = 

1- length of ab:

ab =   = 5 units

2- length of ac

length of ac is the same as ab = 5 units

3- length of bc:

bc =   =  √10  units

now, we can get the perimeter by adding the side lengths as follows:

perimeter = 5 + 5 +  √10

perimeter = 10 +  √10  units

hope this : )

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