Question

The Foster family just hired a landscaping company to put in a flower garden in their backyard. They would like to have a walkwayaround the garden. The picture below represents the flower garden and the surrounding walkway• Write an expression in simplest form that represents the perimeter of the structure.• Write an expression in simplest form that represents the area of the entire structure.• Write an expression in simplest form that represents the area of the garden.• Write an expression in simplest form that represents the area of the walkway.

Answer 1

Remember the formula for perimeter of a rectangle is

P = 2( l+w) where l is length and w is width

Assuming structure is garden and walkway

P = 2( x-3 + 2x+10)

Combine like terms

P = 2( 3x+7)

Distribute

P = 6x+14

The area of a rectangle is found by

A = l*w where l is length and w is width

A = ( x-3) ( 2x+10)

FOIL - first outer inner last

= 2x^2 +10x -6x -30

Combine like terms

=2x^2 +4x-30

Now we want the area of the garden

A = l*w where l is length and w is width

A = ( x-5) ( 2x+7)

FOIL - first outer inner last

= 2x^2 +7x -10x -35

Combine like terms

=2x^2 -3x-35

The area of the walkway is the area of the entire structure minus the area of the garden

=2x^2 +4x-30 - ( 2x^2 -3x-35)

Distribute the minus sign

2x^2 +4x-30 - 2x^2 +3x+35

Combine like terms

7x +5