Question

the area of a rectangle gets reduced by 80 square 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 minutes the area will increase by 50 square units find the length and breadth of rectangle​

Answer 1

Given :-

The area of a rectangle gets reduced by 80 square units.

Length is reduced by 5 units and breadth is increased by 2 units.

When we increase the length by 10 units and decrease the breadth by 5 minutes the area will increase by 50 square units.

To Find :-

The length of the rectangle.

The breadth of the rectangle.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area

When the length is reduced by 5 units and breadth is increased by 2 units.

Length = (l − 5)

Breadth = (b + 2)

By the formula,

$\underline{\boxed{\sf Area \ of \ rectangle=Length \times Breadth}}$

By substituting,

Area = (l − 5) × (b + 2)

According to the question,

(l − 5) (b + 2) − lb = −80

2l − 5b = −70   ....(1)

Now, when we increase the length by 10 units and decrease the breadth by 5

Length = (l + 10)

Breadth = (b − 5)

Area = (l + 10) × (b − 5)

As per the given info,

(l + 10) (b − 5) − lb = 50

10b − 5l = 100

2b − l = 20

4b − 2l = 40    ....(2)

Adding equation (1) and (2), we get

−b = −30

b = 30

Therefore, the length and breadth are 40 and 30 units respectively.