Question

A rectangular yard has a length that is 5 feet more than the width. Around the outside of the yard is a path made of bricks that is 3 feet wide.

a) What expression can be used to represent the area of the path?

b) If the area of the yard and the path is 546 sq. ft, find x

c) What is the area of the yard?

d) What is the area of the path?
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Answer 1

A) A = X^2 + 11X + 24

B) X = 18 ft

C) 414 ft^2

D) 132 ft^2

Explanation:

A) Width W of yard and path = X + 3

Lenght L of path = X + 5 + 3 = X + 8 ft, therefore,

Area of yard and path = L x W = (X +3) x (X +8)

A = X^2 + 11X + 24

B) if area of the yard and path is 546 ft^2,

546 = X^2 + 11X + 24

X^2 +115X - 522 = 0 (quadratic equation)

Solving the quadratic equation gives

X = 18 and X = -29

Our answer can only be positive so we choose X = 18 ft

C) lenght of yard = 5 + 18 = 23 ft

Width = 18 ft

Therefore area = L x W = 23 x 18 = 414 ft^2

D) area of path = area of path and yard minus area of yard

= 546 - 414 = 132 ft^2