Question

the area of a small rectangular plot is 84m^2. if the difference between its length and breadth is 5 m find its perimeter​

Answer 1

Answer:

38 m

Step-by-step explanation:

Let length be l and breadth be b

l - b = 5

l = 5+b    - (i)

Area = 84 m²

l × b = 84

(5+b)(b) = 84             - [from (i)]

5b + b² = 84

b² + 5b  - 84 = 0

b² + 12b - 7b - 84 = 0        [12 ×7 = 84]

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

so b = -12 and b = 7

Since breadth can't be negative, so b = 7 m

Putting b in (i)

l = b + 5

l = 7 + 5 = 12 m

Perimeter of rectangle = 2 (l + b)

                                      = 2 (7 + 12)

                                      = 2 (19)

                                       = 38 m

Ans. Perimeter of the rectangle is 38 m.

Here is your answer

Cheers!

Answer 2

Given:-

• The area of rectangular plot is 84m².
• The difference between length and breadth is 5m.

To Find:-

• Find the length and breadth of rectangle.

Solution:-

Let the length of rectangle be ' x '

Breadth be ' x - 5 '

Then,

Area of rectangle = l × b

84 = ( x ) ( x - 5 )

= x² - 5x - 84

So,

a = 1 ; b = -5 ; c = -84

$\tt \implies { \: \frac{ - b \: ± \: \sqrt{b² \: - \: 4ac \: } }{ \: 2a \: } }$

$\tt \implies { \: x \: = \: \frac{ 5 \: ± \: \sqrt{ 25 \: - \: 336 \: } }{ \: 2 \: } }$

$\tt \implies { \: \frac{ \: 5 \: + \: 19 \: }{2} } \: \: \: \: and \: \: \: \tt { \: \frac{ \: 5 \: - \: 19 \: }{2} }$

$\tt \implies { \: \frac{ \: 24 \: }{2} } \: \: \: \: and \: \: \: \tt { \: \frac{ \: -14 \: }{2} }$

$\tt \implies { \: x \: = \: 12 \: \: and \: - 7 \: }$

$\tt { \: Let \: us \: take \: x \: = \: 12 \: }$

$\tt { \: Then, \: }$

$\tt \implies { \: 84 \: = \: 12 \: × \: 12 \: - \: 5 \: }$

$\tt \implies { \: 84 \: = \: 12 \: × \: 7 \: }$

$\boxed{\bf{\color{yellw}{ \: 84 \: = \: 84 \: }}}$

So,

Length of rectangle = 12

Breadth of rectangle = 7