There is a rectangular lot in the garden, with 7 ft in length and 5 ft in width. You plan to expand the lot by an equal length around its four sides, and make the area of the expanded rectangle 143 ft2. How long should you expand the original lot in four directions?

Question

Mathematics

Alessandra Beasley

17 September, 10:11

There is a rectangular lot in the garden, with 7 ft in length and 5 ft in width. You plan to expand the lot by an equal length around its four sides, and make the area of the expanded rectangle 143 ft2. How long should you expand the original lot in four directions?

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Answers (1)

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Sydney Clements · Answer 1

3 ft at each end

Step-by-step explanation:

The lot area is 7 x 5 = 35ft2

The planned lot area = 143ft2

The plan is to extend the lot by equal length on both the width and the length therefore we can express the extension as y the planned lot can be express as

(5+y) x (7+y) = 143

y2 + 12y + 35 = 143

y2 + 12y - 108 = 0 expand the equation

y2 + 18y - 6y - 108 = 0 factorise the equation

(y-6) (y+18) = 0

(y-6) = 0 or (y + 18) = 0

y = 6. or y = - 18

Length can only be a positive number hence y = 6

However we need to note that we are increasing the 4 directions a length has 2 end so increasing at both end implies

6/2 = 3 ft at each end