Question

4. The area of a small rectangular plot is 84 m2
If the difference between its length and the
breadth is 5 m; find its perimeter.​

Answer 1

Given -

• Area of rectangular plot = 84m²

• Difference between their length and breadth is 5m

To find -

• It's perimeter

Solution -

Let the length be x m

So, the breadth will be x - 5 m

Now,

Area of rectangle = L × B

Where,

L = length

B = breadth

On substituting the values -

Area = L × B

84 = x × (x - 5)

84 = x² - 5x

x² - 5x - 84 = 0

x² + 7x - 12x - 84 = 0

x(x - 12) + 7x(x - 12) = 0

x - 12 = 0

→ x = 12

x + 7 = 0

→ x = 0 - 7

→ -7

As side cannot be negative, x = 12

So,

Length of rectangular plot is 12m

Breath of rectangular plot = x - 5 = 12 - 5 = 7m

Now,

Perimeter of rectangle = 2(l + b)

Perimeter = 2(12 + 7)m

Perimeter = 2(19)m

Perimeter = 38m

$\therefore$ The perimeter of rectangular plot is 38m

Verification -

Area of rectangle = L × B

Area = 12m × 7 m

Area = 84m²

Perimeter of rectangle = 2(l + b)

Perimeter = 2(12 + 7)m

Perimeter = 2(19)m

Perimeter = 38m

LHS = RHS

Hence, proved

___________________________________________________________________________

Answer 2

Answer:

Given

• Area = 84 m²
• Difference between length and breadth = 5

To Find :-

Perimeter

Solution :-

Let the Length be x

As we know that

Area = l×b

$\sf \bull \: 84 = x \times (x - 5)$

$\sf \bull84 = {x}^{2} - 5$

$\sf \bull \: x {}^{2} - 5x - 84 = 0$

$\sf \bull x {}^{2} + 7x - 12x - 84 = 0$

$\sf \bull \: x(x - 12) + 7x(x - 12) = 0$

$\sf \bull \: x - 0 = 12$

$\sf \bull \: x = 12 + 0 = 12$

$\sf \bull \: x + 7 = 0$

$\sf \bull \: x = 7 - 0 = - 7$

Length can't be negative.

Length of rectangular plot = 12m

Breadth of rectangular plot = x - 5 = 12 - 5 = 7m

$\rule{99}{15}$

Perimeter of rectangle = 2(l+b)

Perimeter = 2(12+7)

Perimeter = 2(19)

Perimeter = 38 m