Taylor purchased a rectangular plot of area 634 m2. The length of the plot

Question

Taylor purchased a rectangular plot of area

634 m^{2}

. The length of the plot is 2 m more than thrice its breadth. The length and breadth respectively is _____ (approximate values).

Options:

A . 34.6 m & 11.20 m

B . 88 m & 24 m

C . 32 m & 16 m

D . 44.6 m & 14.20 m

Answer: Option D
:
D
Let, Length =

x

Breadth =

y

Given,
Area of Rectangle =

634 m^{2}

Length :

x

Thrice the breadth:

3 y

2 more that thrice :

3 y + 2

So,

x = 3 y + 2

Area oftherectangle = length \times breadth

634 = x y 634 = (2 + 3 y) y 634 = 2 y + 3 y^{2} ∴ 3 y^{2} + 2 y - 634 = 0

This equation resembles the general form of quadratic equation

a x^{2} + b x + c = 0.

Lets find the values of

y

satisfying the equation.(Roots of the equation)

y = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} = \frac{- 2 \pm \sqrt{2^{2} - 4 \times 3 (- 634)}}{2 \times 3} y = \frac{- 2 \pm \sqrt{4 + 7608}}{6} = \frac{- 2 \pm \sqrt{7612}}{6} y = \frac{- 2 \pm 87.246}{6} y = \frac{- 2 + 87.246}{6} or \frac{- 2 - 87.246}{6} y = 14.20 or - 14.87

Length is always positive.

∴ y = 14.20 m

x = 2 + 3 y ∴ x = 2 + 3 (14.20) = 44.6 m

Length

= 44.6 m

Breadth

= 14.2 m

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