A rectangular garden has a length that is 5 meters longer than its width. If the width is represented by w meters: i. Write an expression for the length of the garden. ii. Write an expression for the perimeter of the garden. iii. Write an expression for the area of the garden. c. If the width of the garden is 8 meters, calculate the perimeter and area.
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4 partsStep-by-step solution
10 stepsPart i· 2 steps
Write an expression for the length of the garden.
Define the given width.
The width of the garden is represented by meters.
Formulate the length based on the problem description.
The length is 5 meters longer than its width.
The expression for the length is .
Part ii
Write an expression for the perimeter of the garden.
Recall the formula for the perimeter of a rectangle.
The perimeter of a rectangle is given by .
Substitute the expressions for length and width into the formula.
We have and width .
Simplify the expression.
The expression for the perimeter is .
Part iii
Write an expression for the area of the garden.
Recall the formula for the area of a rectangle.
The area of a rectangle is given by .
Substitute the expressions for length and width into the formula.
We have and width .
Simplify the expression.
The expression for the area is .
Part c
If the width of the garden is 8 meters, calculate the perimeter and area.
Substitute meters into the perimeter expression from part (ii).
The perimeter is .
Substitute meters into the area expression from part (iii).
The area is .
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