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

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 30m and 20m.

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 30m or 20m

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