A children's park 350 m long and 200 m wide. It is surrounded by a pathway of uniform width. Suppose the total area of the park and the pathway is 74,464 msq. How wide is the pathway?
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4 meters is the width of the pathway.
Step-by-step explanation:
Given that,
Length = 350m
Width = 200m
The total area of the pathway = 74,464m sq.
Let the width of the pathway be x giving the equation
(350 + 2x) (200 + 2x)
As we know that,
A = l * w
74,464 = (350 + 2x) (200 + 2x)
74,464 = 70,000 + 700x + 400x + 4x^2
74,464 - 74,464 = 4x^2 + 1100x - 4464
0 = 4(x^2 + 275x - 1116)
0 = 4(x-4) (x + 279)
∵ x = 4 or x = - 279
A negative number cannot be the width. So, the width of the pathway is 4meters.
Learn more: area of a circle is 616 sq meter there is a pathway of 2m width outside the circle find the area of pathway
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