Question

the area of a rectangle producers by 160 metre square if its length is increased by 5 M and breadth is reduced by for four metre. however if length is decreased by 10 M and breadth is increased by 2 m then its area is increased by hundred metre square find the dimensions of the rectangle....​

Answer 1

Let :-

• Dimensions of rectangle
• Length of rectangle = L
• Breadth of rectangle = B

To Find :-

• The dimensions of rectangle = ?

Solution :-

• To calculate the dimensions of rectangle at first we have to set up equation by applying formula.

Given in case -(i) :-

• the area of a rectangle producers by 160 metre square if its length is increased by 5 M and breadth is reduced by for four metre

↠ Area of rectangle = Length × Breadth

↠ L × B = (L + 5) × (B - 4) + 160

↠ LB = LB + 5B - 4L - 20 + 160

↠ LB - LB + 4L - 5B = -20 + 160

↠ 4L - 5B = 140 --------(i)

Given in case -(ii) :-

• if length is decreased by 10 M and breadth is increased by 2 m then its area is increased by hundred metre square

↠ Area of rectangle = Length × Breadth

↠ L × B = (L - 10) × (B + 2) + 100

↠ LB = LB + 2L - 10B - 20 + 100

↠LB - LB + 2L - 10B = 20 - 100

↠ 2L - 10B = - 80 -------(ii)

• In eq (i) × by 2 and eq (ii) × by 4

↠8L - 10B = 280

↠8L - 40B = -320

• By solving we get here :-

↠30B = 600

↠ B = 20m

• Putting the value of B = 20 in eq (ii)

↠ 2L - 10B = - 80

↠ 2L - 10(20) = - 80

↠2L - 200 = - 80

↠ 2L = - 80 + 200

↠ 2L = 120

↠ L = 60m

Hence,

• The length of rectangle = 60 m
• The breadth of rectangle = 20 m

Answer 2

Step-by-step explanation:

Given:-

• The area of a rectangle producers by 160 metre square if its length is increased by 5 M and breadth is reduced by for four metre. however if length is decreased by 10 M and breadth is increased by 2 m then its area is increased by hundred metre square.

To Find:-

• The dimensions of the rectangle

Solution:-

Let the length and breadth of the rectangle be l and b respectively.

1st condition -

Area of given rectangle = length × breadth

➟ lb m²

New length = l + 5

New Breadth = b - 4

New area = (l + 5)(b - 4)

➻ lb + 5b - 4l - 20

So,

➨ lb = lb + 5b - 4l - 20 + 160

➨ 4l - 5b = 140 ----(i)

2nd condition -

New length = l - 10 m

New breadth = b + 2 m

New area = (l - 10)(b + 2)

⤐ lb + 2l - 10b - 20

So,

➳ lb = lb + 2l - 10b - 20 + 100

➳ 2l - 10b = -80 ----(ii)

Multiply (ii) by 2 and then subtracting it from (i)

(2l - 10b = -80)2

⤕4l - 20b = -160

So,

4l - 5b = 140

4l - 20b = -160

- + +

____________

15b = 300

b = 20

Putting the value of 'b' in eq. 1

4l - 5(20) = 140

4l - 100 = 140

4l = 240

l = 60

So,

❒ Length = 60 m

✇ Breadth = 20 m

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