Question

A rectangular Park of perimeter 80m and area400m square .find it's length and breadth.

Answer 1

Given:

• Perimeter of rectangular Park = 80m
• Area of the rectangular Park = 400 m²

To Find :

• Length (l)
• Breadth (b)

Formula used :

$Perimeter \: of \: rectangle = 2 \times (l + b)$

$Area \: of \: rectangle = l \times b$

Solution :

According to the question,

Perimeter = 2×(l+b)

80 = 2×(l+b)

40 = (l+b) _____________Equation 1

And,

Area = l×b

400 = l×b ______________Equation 2

Now,

l + b = 40

l = (40-b) ______________Equation 3

Putting Equation 3 in Equation 2, we get

→400 = (40-b)×b

→400 = 40b - b²

→b ² - 40b - 400 = 0

On solving this quadratic equation,

→b² - 20b - 20b - 400 =0

→b (b-20) - 20(b-20) = 0

→(b - 20)(b-20) = 0

→b = 20 m

So by using the value of b in Equation 1, we have

→ l + b = 40

→ l + 20 = 40

→ I = 40 - 20 = 20 m

Therefore, the length of the rectangular Park is 20 m and its breadth is also 20 m.

Answer 2

GIVEN:

• Area of rectangular park = 400m²
• Perimeter = 80m

TO FIND:

• Length (l)
• Breadth (b)

SOLUTION:

Using

♦ Area$_Rectangle$ = 2(l + b)

♦ Perimeter$_Rectangle$ = l × b

→ 2(l + b) = 80m

→ l + b = 80/2

→ l + b = 40m---------(1)

→ l×b = 400

→ l = 400/b

Substituting l = 400/b in equation 1

→ 400/b + b = 40

→ 400 + b²/b = 40

→ 400 + b² = 40b

→ b² - 40b + 400 = 0

We get a quadratic equation

→ b² - 2(20)b + 20² = 0

It's in the form of (a - b)² = a² - 2ab + b²

→ (b - 20)² = 0

→ b = 20

Hence, breadth = 20m

Finding : Length

2(l + b) = 80m

→ 2l + 2(20) = 80

→ 2l = 80 - 40

→ 2l = 40

→ l = 40/2

→ l = 20

Hence, Length = 20m & Breadth = 20m