A concrete walk of uniform width is to be laid around a rectangular flower bed that is 60 feet long and 30 feet wide. If the area of the walk is to be 279 square feet, what is the width of the walk?

Question

Mathematics

Celeste

14 February, 06:35

A concrete walk of uniform width is to be laid around a rectangular flower bed that is 60 feet long and 30 feet wide. If the area of the walk is to be 279 square feet, what is the width of the walk?

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Josephine Grant · Answer 1

We know that the area of the flower bed is 60 x 30 = 1800 sqft and that the area of the walk is 279 sqft. We will make an equation that represents the two areas added together so we must add 2x to 30 ft and 2x to 60 ft to include the width of the walk that is of equal width all around that is the 2x. So we get,

(30 + 2x) (60 + 2x) = 279 + 1800 then we simplify to 4x^2 + 180x-279=0, factor to (2x-3) (2x+93) = 0. Now we solve for x. 2x-3=0 gives us x=1.5 and 2x-93=0 gives us - 93/2 which is negative and we know distance is positive so that solution is omitted. We get that the width around the flower garden is 1.5 ft.