A path of uniform width x metres surrounds a rectangular lawn 20 m by 10 m. The total area of lawn plus path is 336 sq m, giving 4x^2 + 60x - 136 = 0, i.e. x^2 + 15x - 34 = 0. Find the width x of the path in metres.

Question

Accepted Answer

2. Outer area (20+2x)(10+2x) = 336 => 200 + 60x + 4x^2 = 336 => 4x^2 + 60x - 136 = 0 => x^2 + 15x - 34 = 0. x = -15 ± √225 + 1362 = -15 ± 19/2 = 2. Width = 2 m.

A path of uniform width $x$ metres surrounds a rectangular lawn 20 m by 10 m.
The total area of lawn plus path is 336 sq m, giving $4 x^{2} + 60 x - 136 = 0$ , i.e. $x^{2} + 15 x - 34 = 0$ .
Find the width $x$ of the path in metres.

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More Class 10 The Quadratic Formula practice

A path of uniform width x metres surrounds a rectangular lawn 20 m by 10 m.The total area of lawn plus path is 336 sq m, giving 4x2+60x−136=0, i.e. x2+15x−34=0.Find the width x of the path in metres.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 The Quadratic Formula practice

A path of uniform width $x$ metres surrounds a rectangular lawn 20 m by 10 m.
The total area of lawn plus path is 336 sq m, giving $4 x^{2} + 60 x - 136 = 0$ , i.e. $x^{2} + 15 x - 34 = 0$ .
Find the width $x$ of the path in metres.