Question

The area of a rectangle reduces by 160 m2if its length is increased by 5 m and breadth is reduced by 4 m. However if length is decreased by 10 m and length is decreased by 10 m and breadth is increased by 2 m, then its area is decreased by 100 m2. Find the dimensions of the rectangle. okay fast ​

Answer 1

Given :-

• If length is increased by 5m and breadth is reduced by 4m, area of the rectangle reduces by 160m².
• If length is decreased by 10m and breadth is increased by 2m, area of the rectangle reduces by 100m².

To Find :-

• Dimensions of the rectangle(length & breadth).

Solution :-

Let:-

• Length = l m.
• Breadth = b m.
• Area = l × b m²

Case I :

When l = l + 5, b = b - 4, Area = lb - 160

⇒ (l + 5)(b - 4) = lb - 160

⇒ lb - 4l + 5b - 20 = lb - 160

⇒ -4l + 5b = -140

⇒ 4l - 5b = 140........( 1 )

Case II :

When l = l - 10, b = b + 2, Area = lb - 100

⇒ (l - 10)(b + 2) = lb - 100

⇒ lb + 2l - 10b - 20 = lb - 100

⇒ 2l - 10b = -80.......( 2 )

Multiplying ( 2 ) with 2, we get,

⇒ 4l - 20b = -160.....( 3 )

Subtracting ( 3 ) from ( 1 ) gives,

⇒ 15b = 300

⇒ b = 300/15

⇒ b = 20 m

Substituting value of b in ( 1 ) gives,

⇒ 4l - 5 × 20 = 140

⇒ 4l - 100 = 140

⇒ 4l = 240

⇒ l = 240/4

⇒ l = 60 m.

Hence,

• Length of the rectangle = 60 m.
• Breadth of the rectangle = 20 m.

Answer 2

Step-by-step explanation:

lb−(l+5)(b−4)=160.

4l−5b=140...1

lb−(l−10)(b+2)=100

10b−2l=140....2

Put l=5b−70 in 1

20b−280−5b=140

15b=420

b=28m

l=70m

Length of rectangle =70m

Breath of rectangle =28m