Question

The length of a rectangular field is 30 m more than its breadth. If the perimeter is 6
4
0
m. Find the l
ength of the rectangular field.
​

Answer 1

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Correct Question :-

• The length of a rectangular field is 30 m more than its breadth. If the perimeter is 640 m. Find the length of the rectangular field.

$\text{\large\underline{\red{Given:-}}}$

• Length of the rectangular field is 30 m more than its breadth.
• Perimeter of the rectangular field = 640 m.

$\text{\large\underline{\pink{To find:-}}}$

• The length of the rectangular field.

$\text{\large\underline{\orange{Solution:-}}}$

• Let the breadth of the rectangular field be x m.
• Then, its length = (x+30) m

We know that,

$\bigstar{\boxed{ \tt{Perimeter \: of \: rectangle = 2(length + breadth)}}} \bigstar$

According to Question,

$\begin{gathered}: \implies {\sf{Perimeter = 640}} \\ \\ : \implies {\sf {2[(x+30)+ x]= 640}} \\ \\ : \implies {\sf {2(x+30+ x)= 640}} \\ \\ : \implies {\sf {2(2x+30)= 640}} \\ \\ : \implies {\sf {4x+60= 640}} \\ \\: \implies {\sf {4x= 640 - 60}} \\ \\ \ : \implies {\sf {4x= 580}} \\ \\ : \implies {\sf {x= \frac{580}{4}}} \\ \\ : \implies { \boxed{\tt {x= 145}}}\end{gathered}$

$\underline {\bf{\therefore{The \:length\: of\: the \:rectangular\: field \:is\:(145+30)\:m = 175\:m.}}}$

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Answer 2

Question:-

The length of a rectangular field is 30 m more than its breadth. If the perimeter is 640 m. Find the length of the rectangular field.

Answer:-

• The length of rectangular field is 175 m

To find:-

• Length of rectanglular field

Solution:-

• Perimeter of rectangle = 640 m

Let,

• Length = x+30 m
• Breadth = x m

As we know,

$\large{ \boxed{ \mathfrak{ perimeter = 2(l + b)}}}$

Where,

• L = length of rectangle
• b = breadth of rectangle

According to question,

$\large{ \tt : \implies \: \: \: \: \: 2(30 + x + x) = 640}$

$\large{ \tt : \implies \: \: \: \: \: 30 + 2x = \frac{640}{2} }$

$\large{ \tt : \implies \: \: \: \: \: 30 + 2x = 320}$

$\large{ \tt : \implies \: \: \: \: \: 2x = 320 - 30}$

$\large{ \tt : \implies \: \: \: \: \: 2x = 290}$

$\large{ \tt : \implies \: \: \: \: \: x = \frac{290}{2} }$

$\large{ \tt : \implies \: \: \: \: \: x = 145}$

• The value of x is 145 m

• Length = x +30 = 145+30 = 175 m
• Breadth = x = 145 m

Hence,

The length of rectangular field is 175 m