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Quadratic Equations — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsQuadratic Equations1 Mark
MCQ
A rectangular field is $16m$ long and $10m$ wide. There is a path of uniform width all around it having an area of $120\text{sq. m},$ then the width of the path is :
  • A
    $4m$
  • B
    $5m$
  • ✓
    $2m$
  • D
    $3m$
✓

Answer

Correct option: C.
$2m$
Let the width of the path be $x$ meter
$\therefore$ Area of path $= $ Area of $\text{ABCD} -$ Area of $\text{PQRS}$ 
$\Rightarrow 120 = (16 + 2x) (10 + 2x) -16 \times 10$
$\Rightarrow 120 = 160 + 32x + 20x + 4x2 - 160$
$ \Rightarrow 4 x^2+52 x-120=0 $
$ \Rightarrow x^2+13 x-30=0 $
$ \Rightarrow x^2+15 x-2 x-30=0 $
$\Rightarrow x(x + 15) -2(x + 15) = 0$
$\Rightarrow (x + 15) (x - 2) = 0$
$\Rightarrow x + 15 = 0$ and $x - 2 = 0$
$\Rightarrow x = -15$ and $x = 2 [x = -15$ is not possible$]$
$\therefore$ The width of the path is $2m$.

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