Question

find perimeter of a rectangular field whose length is 4 times its width and which has area equal to 20736 square meters

Answer 1

Let the width be x ,then length is 4x.
We know,
Area of rectangle=l*b
Therefore,area=4x*x
20736=4x^2
144=2x
x=72.
Therefore ,perimeter=2(l+b)
=2(4*72+72)
=2(288+72)
=2*360=720 

Answer 2

Answer:

Area of a rectangle(A) is given by:

$A= l \cdot w$          ....[1]

where l is the length and w is the width of the rectangle respectively.

As per the statement:

Length of rectangle is 4 times its width and which has area equal to 20736 square meters.

⇒$l =4w$

Substitute the value of A = 20736 square meter and l =4w in [1] we have;

$20736=4w \cdot w$  

or

$20736 = 4w^2$

Divide both sides by 4 we have;

$5184=w^2$

⇒$w = \sqrt{5184}$

Simplify:

w = 72 meter.

then;

$l =4(72)=288$ meter.

Perimeter of rectangle(P) is given by:

$P=2(l+w)$

Substitute the value of l and w we have;

$P=2(288+72) = 2(360)=720 cm$

Therefore, the value of perimeter of a rectangular field is, 720 cm