Question

A vacant rectangular lot is being turned into a community vegetable garden with a uniform path around it. area of the lot is represented by 4x^2 40x - 44 where x is the width of the path in meters. Find the wisdom the path surrounding the garden.

Answer 1

By factorizing the expression, 4x² + 40x - 44, the width of the path (x) is calculated as: 11 meters.

How to Factorize an Expression?

To factorize an expression, such as 4x² + 40x - 44, we need to determine the two factors that will give us -176 when multiplied, and also give us 40 when added.

To find the width of the path, x, we need to factorize 4x² + 40x - 44, using the two factors, 4 and -44.

4x² - 44x + 4x - 44

(4x² - 44x) + (4x - 44)

4x(x - 11) + 4(x - 11)

(x - 11)(4x + 4) = 0

x = 11 or x = -4/4 = -1

The value of the width of the path, x, cannot be negative. Therefore, the width of the path would be: 11 meters.

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