A square garden (green) of 400 m 2 is to be surrounded by a walkway (yellow) of constant width x. the total area of the walkway has to be 500 m 2. find the width x of the walkway.
Answers
Given:
A square garden (green) of 400 m² is to be surrounded by a walkway (yellow) of constant width x.
The total area of the walkway has to be 500 m²
To find:
The width of the walkway
Solution:
The area of the square garden = 400 m²
Let "a" represent each side of the square garden.
∴ side² = a² = 400
⇒ a = √400
⇒ a = 20 m
Since the width of the walkway is given as "x" meter, so
The length of the side of the square garden (including the walkway) is,
= a + x + x
= (20 + 2x) m
∴ Area of the square garden (including the walkway) = (20 + 2x)² m²
Now, we can say that,
Area of the walkway = [Area of the square garden (including the walkway)] - [Area of the square garden]
substituting the values, we get
⇒ 500 m² = [(20 + 2x)² m²] - [400 m²]
⇒ 500 + 400 = (20 + 2x)²
⇒ 900 = 400 + 80x + 4x²
⇒ 4x² + 80x + 400 - 900 = 0
⇒ 4x² + 80x + 500 = 0
⇒ 4x² + 100x - 20x - 500 = 0
⇒ 4x(x + 25) - 20(x + 25) = 0
⇒ (x + 25)(4x - 20) = 0
⇒ x = -25 or x = = 5
the width of the walkway cannot be in negative so we will ignore the negative value
⇒ x = 5 m
Thus, the width "x" of the walkway is → 5 m.
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Answer:
Step-by-step explanation: