Question

the perimeter of a rectangular plot is 42 metres and its area is 108 CM square find the dimensions of the plot​

Answer 1

Answer:

$\huge\fcolorbox{black}{pink}{Answer-}$

l

Step-by-step explanation:

Given :

perimeter of the rectangle = 42 m

area of the rectangle = 108 cm^2

To find :

Dimensions of the rectangle .

Proof :

Let l and b the sides of the rectangle .

Therefore ,

According to the conditions ,

perimeter = 2 ( l+ b)

42 = 2 ( l + b )

21 = l + b

l = 21 - b ----(1)

area = l × b

108 = l × b ---(2)

substituting eq (1) in eq (2)

108 = (21 - b ) b

108 = 21 b - b^2

b^2 + 108 - 21b = 0

b^2 - 21b + 108 = 0

b^2 - 12b -9b + 108 =0

b ( b - 12 ) - 9(b - 12 ) = 0

( b - 12 ) ( b - 9 ) =0

Therefore ,

b = 12 and b = 9

Case 1

b = 12

substituting b = 12 in eq (1 )

l = 21 - 12

l = 9

Case 2

b = 9

substituting b = 9

l = 21 -9

l = 12

Answer 2

Step-by-step explanation:

$\huge \mathcal{Answer - }$

$\bold{Given -} \\ \\ \bold{Perimeter \: of \: rectangular \: plot = 42 \: m} \\ \bold{Area \: of \: rectangular \: plot = 108 \: {m}^{2} } \\ \\ Now, \\ According \: to \: question \\ \\ \bold{ 2(l + b) = 42} \\ l + b = 21 \\ \\ \bold{ l \times b = 108} \\ \\ \fbox\bold{ b = \frac{108}{l} } \\ \\ Substituting \: \bold{b = \frac{108}{l} } \: on \: \bold{l + b = 21} \\ \\ l + \frac{108}{l} =21 \\ \\ \frac{ {l}^{2} + 108}{l} = 21 \\ \\ {l}^{2} + 108 = 21l \\ \\ \bold{l {}^{2} - 21l + 108} \\ \\ Now \: factorising \: this, \\ \\ l {}^{2} - 9l - 12l + 108 \\ l(l - 9) - 12(l - 9) \\ (l - 12)(l - 9) \\ \\ l - 12 = 0 \: \: \: \: \: and \: \: l - 9 = 0 \\ \\ \fbox\bold{l = 12 \: \: \: and \: \: \: l = 9} \\ \\ Substituting \: the \: value \: of \: \bold{l = 9} \: on \: \bold{l + b = 21} \\ \\ \bold{9} + b = 21 \\ b = 21 - 9 \\ \\ \fbox\bold{b = 12} \\ \\ \\ Hence, \\ \fbox \bold{Length = 9 \: m} \\ \bold{and} \\ \fbox\bold{Breadth = 12 \: m}$