Algebra

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You are planning to build a walkway that surrounds a rectangular garden that is 10ft by 9ft. The width of the walkway around the garden is unknown, but it will be the same on every side.
a)what is the perimeter of the walkway along the outer edge ?
b) what is the combined area of the garden and the walkway ?
c)find the combined area when the width of the walkway is 4ft

• Algebra -

garden:
length = 10 ft
width = 9 ft

garden including walkway:
length = 10+2x
width = 9+2x

a) perimeter = 2(10+2x) + 2(9+2x)
= 20 + 4x + 18 + 4x
= 8x + 38

b) area of whole thing
= (10+2x)(9+2x)
= 90 + 38x + 4x^2

c) when x=4
area according to formula = 90 + 38(4) + 4(4^2) = 306

area using arithmetic:
length = 18
width = 17
area = 18x17=306

• Algebra -

The length of a rectangular rug is twice its width. The rug is centered in a rectangular room. Each edge is 3ft. From the nearest wall. What is the area of the room?

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