Question

Help me to solve this ​

Answer 1

$\mathcal \pink {{SOL:-}}$

let the length and breadth of rectangle be x and y.

According the first condition :-

A = l × b = xy ✅ ....Area of rectangle

l = (x + 3), b = (y - 4) and A = xy - 67

$\tt \red {now,}$

•°• (x + 3) × (y - 4) = xy - 67

x(y - 4) + 3(y - 4) = xy - 67

xy - 4x + 3y - 12 = xy - 67

-4x + 3y = -67 + 12

4x - 3y = 67 - 12

4x - 3y = 55 ...........(a)

According to the second Condition:-

l = (x - 1), b = (y + 4) and A = xy + 89

$\tt \red {now,}$

(x - 1) × (y + 4) = xy + 89

x(y + 4) - 1(y + 4) = xy + 89

xy + 4x - y - 4 = xy + 89

4x - y = 89 + 4

4x - y = 93 .........(b)

solving equation a and b:-

subtracting equation a from b

4x - y = 93

-(4x - 3y = 55)

2y = 38

y = 38/2

y = 19

substituting y = 19 in equation a:-

4x - 3×19 = 55

4x - 57 = 55

4x = 55 + 57

4x = 112

x = 28

Dimension

length = 28 , breadth = 19

Answer 2

let the length and breadth of rectangle be x and y.

According the first situation :-

A = l × b = xy ....Area of rectangle

l = (x + 3), b = (y - 4) and A = xy - 67

now,

•°• (x + 3) × (y - 4) = xy - 67

x(y - 4) + 3(y - 4) = xy - 67

➬xy - 4x + 3y - 12 = xy - 67

➬-4x + 3y = -67 + 12

➬4x - 3y = 67 - 12

➬4x - 3y = 55 ...........(eq 1)

According to the second situation:-

l = (x - 1), b = (y + 4) and A = xy + 89

now,

(x - 1) × (y + 4) = xy + 89

➬x(y + 4) - 1(y + 4) = xy + 89

➬xy + 4x - y - 4 = xy + 89

➬4x - y = 89 + 4

➬4x - y = 93 .........(eq 2)

solving equation a and b:-

subtracting equation 1 from 2

4x - y = 93

➬-(4x - 3y = 55)

➬2y = 38

➬y = 38/2

➬y = 19

substituting y = 19 in equation 1:-

4x - 3×19 = 55

➬4x - 57 = 55

➬4x = 55 + 57

➬4x = 112

➬x = 28

So, length = 28 , breadth = 19.

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