Question

The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and
breadth is increased by 2 units. If we increase the length by 10 units and decrease the
breadth by 5 units then the area will be increased by 50 sq units. Find the length and
breadth of the rectangle.​

Answer 1

Answer:

Let length and Breadth be l,b

and the Area be A=l∗b.............(1)

Now, According to Question

A−80=(l−5)(b+2)⇒A−80=lb+2l−5b−10⇒2l−5b=−70................(2) (Since, A=l*b)

Similarly,

A+50=(l+10)(b−5)⇒A+50=lb−5l+10b−50⇒10b−5l=100..............(3)

Solving (2) and (3)

we get, l=40,b=30

Step-by-step explanation:

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Answer 2

• Length of the rectangle = 40 unit .
• Breadth of rectangle = 30 unit .

Step-by-step explanation:

Given :-

• The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and breadth is increased by 2 units.
• If we increase the length by 10 units and decrease thebreadth by 5 units then the area will be increased by 50 sq units.

To find :-

★ Find the Length and Breadth of the Rectangle .

Formula used :-

Area of Rectangle = Length × Breadth .

Solution :-

• Let Length of rectangle = x unit .
• Let Breadth of rectangle = y unit .

So,

Area of Rectangle = ( x × y ) unit²

= xy unit² .

Now,

A.T.Q.

The area of a rectangle gets reduced by 80 sq units, if its length is reduced by 5 units and

breadth is increased by 2 units.

So,

( x – 5 ) ( y + 2 ) = xy – 80

xy + 2x – 5y – 10 = xy – 80

xy – xy + 2x – 5y = – 80 + 10

2x – 5y = –70 .........eq.(1)

Now,

If we increase the length by 10 units and decrease the breadth by 5 units then the area will be increased by 50 sq units.

So,

( x + 10 ) ( y – 5 ) = xy + 50

xy – 5x + 10y –50 = xy + 50

xy – xy –5x + 10y = 50 + 50

–5x + 10y = 100 ............eq.(2)

Multiply by 2 in eq.(1) we get --

4x –10y = –140 ...........eq.(3)

Add eq.(2) and eq.(3) we get --

–5x + 10y = 100

4x –10y = –140

– x = – 40

x = 40

Put the value of x = 40 in eq.(2) we get --

⟼ –5x + 10y = 100

⟼ –5 × 40 + 10y = 100

⟼ –200 + 10y = 100

⟼ 10y = 100 + 200

⟼ 10y = 300

⟼ y = 300/10

⟼ y = 30

So,

Length of the rectangle = x = 40 unit

Breadth of the rectangle = y = 30 unit