Question

The area of a rectangular plot is 582 m the length of the plot is one more than twice its breadth find the length and breadth of the plot

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Length=34.6\:m}}}$

$\green{\tt{\therefore{Breadth=16.8\:m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Area \: of \: rectangle = 582 \: {m}^{2} \\ \\ \tt: \implies Length \: of \: plot \: is \: one \: more \: that \: twice \: its \: Breadth \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Length = ? \\ \\ \tt: \implies Breadth = ?$

• According to given question :

$\circ \: \text{Let \: Breadth \: be \: x} \\ \\ \circ \: \text{Length = 1 + 2x} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: rectangle = Length \times Breadth \\ \\ \tt: \implies 582 = (1 + 2x) \times x \\ \\ \tt: \implies 582 = x + 2 {x}^{2} \\ \\ \tt: \implies {2x}^{2} + x - 582 = 0 \\ \\ \tt: \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{ {1}^{2} - 4 \times 2 \times 582 } }{2 \times 2} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{1 + 4656} }{4} \\ \\ \tt: \implies x = \frac{ - 1 \pm \sqrt{4657} }{4} \\ \\ \tt: \implies x = \frac{ - 1 \pm68.2}{4} \\ \\ \tt: \implies x = \frac{67.2}{4} \\ \\ \green{\tt: \implies x = 16.8 \: m} \\ \\ \bold{Note-} \: \tt{ Length \: and \:Breadth \: cannot \: be \: in \: negative} \\ \\ \green{\tt \therefore Length = 1 + 2 \times 16.8 = 34.6 \: m} \\ \\ \green{\tt \therefore Breadth = x = 16.8 \: m}$

Answer 2

Answer:

Given:

• The area of a rectangular plot is 582 m² the length of the plot is one more than twice its breadth.

Find:

• Find the length and breadth of the plot.

According to the question:

• Let us assume 'x' as breadth and '2x + 1' as length.

• Area = 582 m²

• Length = (2x + 1).

Calculations:

⇒ x (2x + 1) = 582

⇒ 2 x² + x = 582

⇒ 2 x² + x - 582 = 0

Finding the length:

⇒ 2x² + x - 582 = 0

⇒ 2x² + 32x + 33x - 582 = 0

⇒ x = -x ± √x²- 4/2x

⇒ x = -1 ± √1² - 4 × 2 × 582/(2 × 2 = 4)

⇒ x = -1 ± √1 + 4656/4

⇒ x = -1 ± 68.2/4 = 16.8

⇒ x = 16.8 m - [Breadth]

Finding the breadth:

⇒ [(1 + 2) × (16.8)]

⇒ 34.6 m - [Length]

Therefore, 16.8 m is the breadth and 34.6 m is the length.