A rectangular meadow has an area of 247 sq.m. and its perimeter is 64m, find the length and breadth of the meadow. | Quadratic Equation | SciPiPupil

Question: A rectangular meadow has an area of 247 sq.m. and its perimeter is 64m, find the length and breadth of the meadow.

Solution:

Given,

Area of the rectangular meadow (A) = 247 m²

Perimeter of the meadow (P) = 64 m

Let the length and breadth of the same rectangular meadow be l m and b m respectively.

We have,

P = 64

$or, 2(l+b) = 64$

$or, 2(l+b) = 2×32$

$or, l+ b= 32$

$or, l = 32-b$ - (i)

Also,

A = 247

$or, lb = 247$

[ Put value of l from equation (i) ]

$or, (32-b)b = 247$

$or, 32b - b² = 247$

$or, b² -32b +247 = 0$

$or, b² -(19+13)b +247 = 0$

$or, b² -19b -13b +247 = 0$

$or, b(b -19) -13(b -19) = 0$

$or, (b -13)(b -19) = 0$

Either

$b -13 = 0$

$\therefore b = 13$

Or,

$b -19 = 0$

$\therefore b = 19$

Since, we take breadth is always shorter than the length. Put value of b = 13 in equation (i), we get,

$l = 32-13$

$\therefore l = 19$

So, (l,b) = (19,13)

Therefore, the required length and breadth of the rectangular meadow are 19m and 13m respectively.

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