A garden measuring 9 meters by 4 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 150 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).

Question

Cassis

Mathematics

8 November, 00:34

A garden measuring 9 meters by 4 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 150 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).

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Answers (2)

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Onyx · Answer 1

3 metres

Step-by-step explanation:

Let the width of the pathway be x

Area: (9+2x) (4+2x)

36 + 8x + 18x + 4x²

4x² + 26x + 36

Increased area is 150:

4x² + 26x + 36 = 150

4x² + 26x - 114 = 0

2x² + 13x - 57 = 0

2x² + 19x - 6x - 57 = 0

x (2x + 19) - 3 (2x + 19) = 0

(x - 3) (2x + 19) = 0

x = 3, x = - 19/2