Question

Area and perimeter of a rectangular park are 600 sq. m and 100 m
respectively. Find the length and breadth of the park.

Answer 1

Answer:

Let length be l and breadth be b

ATQ

2{l + b} = 100

l +  b = 50

L = 50 - b

L * B = 600

50b - b² = 600

b² - 50 b + 600 = 0

b² - 30b - 20b + 600 = 0

B{B - 30} - 20{B - 30} = 0

{B - 30}{B - 20} = 0

B = 20 and not 30 as L is always greater than breadth

L = 30

Answer 2

Given :

• Area of the rectangular park = 600 sq.m
• Perimeter of the rectangular park = 100 m

To Find :

• Length and Breadth of the rectangular park

Solution :

Let the length and breadth of the rectnagular park be "l"

and "b"

Perimeter of a rectangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{Perimeter_{(rectangle)} = 2(l + b)}}}}$

We are given that perimeter of rectangular park as 100 m.

$\\ : \implies \sf \: 100 = 2(l + b)$

$\\ : \implies\sf \: \frac{100}{2} = l + b$

$\\ : \implies \sf \: l + b = 50 \: ......... \: eq(1)$

$\qquad$ ━━━━━━━━━━━━━━━━

Area of a rectangle is given by ,

$\\ \star \: {\boxed{\purple{\sf{area_{(rectangle)} = l \times b}}}}$

We are given that area of the area of ths rectangular park as 600 sq.m

$\\ : \implies \sf \: 600 = lb \:$

$\\ : \implies \sf \: \frac{600}{b} = l \: \: ........ \: eq(2)$

Substituting the value of l in equation(1) ,

$\\ : \implies \sf \: \frac{600}{b} + b = 50$

$\\ : \implies \sf \: \frac{600 + {b}^{2} }{b} = 50$

$\\ : \implies \sf \: 600 + {b}^{2} = 50b$

$\\ : \implies \sf \: {b}^{2} - 50b + 600 = 0$

$\\ : \implies \sf \: {b}^{2} - 20b - 30b + 600 = 0$

$\\ : \implies \sf \: b(b - 20) - 30(b - 20) = 0$

$\\ : \implies \sf \: (b - 30)(b - 20) = 0$

So , Breadth of the rectangular park is 30 m or 20 m.

From equation(1) , Length of the rectangular park when it's breadth is 30 m is ;

$\\ : \implies \sf \: 30 + l = 50$

$\\ : \implies \sf \: l = 50 - 30$

$\\ : \implies{\underline{\boxed {\pink{\mathfrak{l = 20 \: m}}}}} \: \bigstar$

Now , Length of the rectangular park when it's breadth is 20 m is ;

$\\ : \implies \sf \: 20 + l = 50$

$\\ : \implies \sf \:l = 50 - 20$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{l = 30 \: m}}}}} \: \bigstar$

Hence ,

• The length and breadth of the rectangular park are 30 m and 20 m