Question

the length of a rectangular park is 14 cm more than its breadth. if the perimeter of the park is 200 m, what is its length ? find the area of the park.

Answer 1

the area if park is 249951cm2

Answer 2

SOLUTION :

The perimeter of rectangular park = 200 m (given)

200 m = 200 × 100 = 20000 cm

Let

the breadth of the park  be x cm

So, According to the question, the length of the rectangle is 14 cm more than its breadth.

So,

length = (x+14) cm

Now,

We know that,

Perimeter of rectangle = 2(l+b) units

[ ∴ In which l is the length and is the breadth of the rectangle ]

⇒ 20000 = 2(x+14+x)

⇒ 20000 = 2(2x+14)

⇒ 20000 ÷ 2 = 2x +14   [ taking 2 to LHS ]

⇒ 10000 = 2x+14

⇒ 10000 - 14 = 2x

⇒ 9986 = 2x

⇒ 9986 ÷ 2 = x

⇒ 4993 = x

∴ x = 4993

Hence,

breadth of the rectangle = x cm = 4993 cm

length of the rectangle = x+14 cm = 4993+14 + 5007 cm

Now,

Area of the rectangle,

= lb  unit sq.

[ ∴ In which l is the length and b is the breadth of the rectangle ]

= 5007 × 4993 cm sq.

= 24999951 cm sq.

or 2499.99 m sq.