Question

the area of the rectangular plot is 528 m square. the length of the plot is one meter more than twice its breadth.Find the length and breadth of the plot

Answer 1

✬ Length = 33 m ✬

✬ Breadth = 16 m ✬

Step-by-step explanation:

Given:

• Area of rectangular plot is 528 m².
• Length of plot is one meter more than twice the breadth.

To Find:

• What is the length & breadth of plot?

Solution: Let the breadth of rectangular plot be x m. Therefore,

➛ Length = One meter more than twice breadth.

➛ Length = (2x + 1) m

As we know that

★ Area of Rectangle = ( Length $\times$ Breadth ) ★

A/q

• Area = 528 m²

$\implies{\rm }$ 528 = (2x + 1)(x)

$\implies{\rm }$ 528 = 2x² + x

$\implies{\rm }$ 0 = 2x² + x – 528

Now, break the equation by middle term splitting.

➙ 2x² + x – 528

➙ 2x² – 32x + 33x – 528

➙ 2x (x – 16) + 33 (x – 16)

➙ (2x + 33) (x – 16)

➙ (2x + 33) = 0 or (x – 16) = 0

➙ 2x = –33 or x = 16

Since, x cannot be negative so we will take x = 16

Hence,

➫ Breadth = x = 16 m

➫ Length = 2x + 1 = 2(16)+1 = 33 m

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★ Verification ★

→ (Length) (Breadth) = 528 m²

→ (33) (16) m² = 528 m²

→ 528 m² = 528 m²

[ Verified ]

Answer 2

GIVEN:

• The area of the rectangular plot is 528 m square.
• The length of the plot is one meter more than twice its breadth.

TO FIND:

• What is the length and breadth of the plot ?

SOLUTION:

Let the length of the plot be 'l' m and breadth be 'b' m

➣ If the length of the plot is one meter more than twice its breadth.

$\bf{\dashrightarrow l = 2b + 1....1) }$

We know that the formula for finding the area of the rectangular plot is:-

$\large\bf{\star \: Area = Length \times Breadth \: \star}$

According to question:-

Put the value of 'l' in formula

$\rm{\dashrightarrow 528 = (2b+1)b }$

$\rm{\dashrightarrow 528 = 2b^2 + b }$

$\rm{\dashrightarrow 2b^2 + b - 528 = 0 }$

$\rm{\dashrightarrow 2b^2 +(33-32)b -528 = 0 }$

$\rm{\dashrightarrow 2b^2 + 33b - 32b - 528 = 0 }$

$\rm{\dashrightarrow b(2b + 33) -16(2b + 33) = 0}$

$\rm{\dashrightarrow (2b + 33)(b-16)=0 }$

$\rm{\dashrightarrow b = \dfrac{-33}{2} \: (Neglected) }$

$\bf{\dashrightarrow b = 16 \: m }$

Put the value of 'b' in equation 1)

$\rm{\dashrightarrow l = 2 \times 16+1 }$

$\rm{\dashrightarrow l = 32 +1 }$

$\bf{\dashrightarrow l =33 \: m }$

❝ Hence, the length and breadth of the rectangular plot are 33 m and 16 m respectively. ❞

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