The length of a rectangular field is $5$ metres less than twice the breadth. If its area is $700$ square metres, then the perimeter (in metres) of the field is

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Solution

Let length be $l$ and breadth be $b$ , so
$l = 2 b - 5$
Now, the area is
$l b = 700 \Rightarrow (2 b - 5) b = 700 \Rightarrow 2 b^{2} - 5 b - 700 = 0 D = 25 + 5600 = 5625 \Rightarrow b = \frac{5 \pm \sqrt{5625}}{4} \Rightarrow b = \frac{5 \pm 75}{4} \Rightarrow b = - \frac{35}{2}, 20 ∴ b = 20 (∵ Breath cannot be negative) \Rightarrow l = 40 - 5 = 35$

Hence, the perimeter
$= 2 (35 + 20) = 110 m$

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The length of a rectangular field is 5 metres less than twice the breadth. If its area is 700 square metres, then the perimeter (in metres) of the field is

Let length be l and breadth be b, so l=2b−5 Now, the area is lb=700⇒(2b−5)b=700⇒2b2−5b−700=0D=25+5600=5625⇒b=5±√56254⇒b=5±754⇒b=−352,20∴b=20 (∵Breath cannot be negative)⇒l=40−5=35 Hence, the perimeter =2(35+20)=110 m

The length of a rectangular field is $5$ metres less than twice the breadth. If its area is $700$ square metres, then the perimeter (in metres) of the field is