Question

The perimeter of a rectangular field is
60 m. If its length is increased by 3 m
and breadth is decreased by 3 m its
area decreases by 21 sq m. Find the
length and breadth of the field.​

Answer 1

$\Huge{\mathscr{\fcolorbox{navy}{orange}{\color{darkblue}{Question?}}}}$

❣ The perimeter of a rectangular field is 60 m. If its length is increased by 3 m and breadth is decreased by 3 m its area decreases by 21 sq m.Find the length and breadth of the field.

❥ Given :-

➪ Perimeter of the rectangular field = 60 m

➪ Let "x" and "y" be the length and breadth of the rectangular field respectively.

➪ New length of the rectangular field = (x + 3m)

➪ New breadth of the rectangular field = (y - 3m)

Also,

➪ New area of the rectangular field = (original area (xy) - 21 sq. m)

❥ To find :-

➪ The length and breadth of the rectangular field.

$\huge \underbrace \bold\blue{↓Solution☟↓}$

❥ We know that,

➪ Perimeter of a rectangular field = 2 (x + y)

➪ 60 m = 2 (x + y)

➪ x + y = 30 m....(i)

➵ As per the second condition,

➪ (x + 3m) (y -3m) = (xy) - 21

➪ xy - 3x +3y - 9 = xy - 21

➪ - 3x + 3y = - 12

➪ -x + y = - 4...(ii)

➵ On adding equation (i) and (ii), we have

➪ x + y = 30

➪ -x + y = -4

--------------------

➪ 2y = 26

➪ y = 26/2

$\huge{\boxed{\boxed{\tt{\purple{➪ y = 13\: m}}}}}$

➵ Putting the value of "y" in equation (i), we have

➪ x + 13 = 30

➪ x = 30 - 13

$\huge{\boxed{\boxed{\tt{\purple{➪ x = 17\: m}}}}}$

❥ Hence, the length and breadth of the rectangular field are 17 m and 13 m respectively.

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