Question

the area of a rectangle gets reduced by 9 square units. if its length is reduced by 5 units and the breadth is increased by 3 units .if we increase the length by 3 units and breadth 2 units the area is increased by 67 square unit. find the length and the breadth of rectangle.
Step by step answer is required. ​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

• Length of rectangle = x = 17 units
• Breadth of rectangle = y = 9 units

To find:

• length and breadth of the rectangle

Solution:

• Let length of rectangle be x
• Let breadth of rectangle be y

As we know that,

• Area = length × breadth = Area = xy

Given that,

• The area of a rectangle gets reduced by 9 square units. if its length is reduced by 5 units and the breadth is increased by 3 units

so,

• Area = length × breadth

● xy - 9 = x(x - 5) (y + 3)

● xy - 9 = x(y + 3) - 5(y + 3)

● xy - 9 = xy + 3x - 5y - 15

● 0 = xy + 3x - 5y - 15 - xy + 9

● 3x - 5y - 6 = 0

● 3x - 5y = 6

3x - 5y = 6 is equation (1)

Also Given that,

• the area is increased by 67 square unit.
• if we increase the length by 3 units and breadth 2 unit

so,

• Area = length × breadth

● xy + 67 = x(x + 3) (y + 2)

● xy + 67 = x(y + 2) - 3(y + 2)

● xy + 67= xy + 2x - 3y - 6

● 0 = xy + 2x + 3y + 6 - xy + 67

● 2x + 3y - 61 = 0

● 2x + 3y =61

2x + 3y =61 is equation (2)

Here both equation are

• 3x - 5y = 6
• 2x + 3y = 61

Now ,from equation (1),

• 3x - 5y = 6 (1)

● 3x - 5y = 6

● 3x = 6 + 5y

● x = 6 + 5y / 3

Now put the value x in equation (2) ,

● 2x + 3y = 61

● 2 (6+5y)/3) + 3y = 6

Now multiplying both by 3

● 3 × 2 (6+5y)/3 + 3 × 3y = 3 × 61

● 2 (6 + 5y) + 9y = 183

● 12 + 10y + 9y = 183

● 19y = 183 - 12

● 19y = 171

● y = 171 / 19

● y = 9

Now putting the value y = 9 in eq (1),

● 3x - 5y = 6

● 3x - 5(9) = 6

● 3x - 45 = 6

● 3x = 6 + 45

● 3x = 51

● x = 51 / 3

● x = 17

Hence , x = 17 y = 9

• Length of rectangle = x = 17 units
• Breadth if rectangle = y = 9 units