Question

The area of a rectangular plot is 528 m. the length of the plot (in meters) is one more than twice its breadth. We need find the length and breadth of the plot

Answer 1

 let the breadth =b m
length = l =(2b+1)m
area =528m²

l*b= 528
(2b+1)b-528=0

2b²+b-528=0
2b²+33b-32b-528=0
b(2b+33)- 16(2b+33)=0
(2b+33)(b-16)=0
2b+33=0 or b-16=0

b should not be zero
therefore
b-16=0
b=16

breadth = 16m
length =l= 2b+1=2*16+1=32+1=33m

Answer 2

$\huge\sf\pink{Answer}$

☞ Length = 33m

☞ Breadth = 16m

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The area of the rectangular plot is 528 m square

✭ The length of the plot is one meter more than twice its breadth

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Length and the breadth of the plot?

$\rule{110}1$

$\huge\sf\purple{Steps}$

$\bullet\underline{\textsf{\: According to the Question}}$

$\sf{\leadsto l = 2b + 1\qquad -eq(1) }$

Area of a rectangle is given by,

$\underline{\boxed{\sf{\sf Area = Length \times Breadth }}}$

Put the value of l in formula

➝ $\sf{ 528 = (2b+1)b }$

➝ $\sf{ 528 = 2b^2 + b }$

➝ $\sf{ 2b^2 + b - 528 = 0 }$

➝ $\sf{ 2b^2 +(33-32)b -528 = 0 }$

➝ $\sf{ 2b^2 + 33b - 32b - 528 = 0 }$

➝ $\sf{ b(2b + 33) -16(2b + 33) = 0}$

➝ $\sf{ (2b + 33)(b-16)=0 }$

➝ $\sf{ b = \dfrac{-33}{2} }$

➝ $\sf{\orange{ b = 16 \:m }}$

Put the value of 'b' in eq(1)

»» $\sf{ l = 2 \times 16+1 }$

»» $\sf{ l = 32 +1 }$

»» $\sf{\green{l =33 \: m }}$

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