Question

If the length of a rectangle is increased by 2 M and the breadth is decreased by 2M, the area is decreased by 28 Sq. M. If the length is decreased by 1 M and breadth is increased by 2 M, the area is increased by 33 Sq. M. Find the length and breadth.

Answer 1

Given :-

▪ When the length of a rectangle is increased by 2 m and the breadth is decreased by 2 m, then the area is decreased by 28 sq. m.

▪ Also, if the length is decreased by 1 m and breadth is increased by 2 m, then the area is increased by 33 sq. m.

To Find :-

▪ Length and breadth of the triangle.

Solution :-

Let the length and breadth of the triangle be x and y respectively.

So,

⇒ Area of rectangle = Length × Breadth

⇒ Area = x × y

⇒ Area = xy

Now, Case 1:

- Length is increased by 2 m and the breadth is decreased by 2 m. Then area is decreased by 28 sq. m

⇒ (Length + 2) (Breadth - 2) = Area - 28

⇒ (x + 2)(y - 2) = xy - 28

⇒ xy - 2x + 2y - 4 = xy - 28

⇒ - 2x + 2y = - 24

⇒ 2x - 2y = 24

⇒ x - y = 12 ...(1)

Similarly, Case 2:

- Length is decreased by 1 m and breadth is increased by 2 m, then area is increased by 33 sq. m.

⇒ (Length - 1)(Breadth + 2) = Area + 33

⇒ (x - 1)(y + 2) = xy + 33

⇒ xy + 2x - y - 2 = xy + 33

⇒ 2x - y = 33 + 2

⇒ 2x - y = 35 ...(2)

Subtract (2) and (1) , we have

⇒ x - y - (2x - y) = 12 - 35

⇒ x - y - 2x + y = -23

⇒ -x = -23

⇒ x = 23

Now, Put [x = 23] in (1), we get

⇒ 23 - y = 12

⇒ y = 23 - 12

⇒ y = 11

Hence,

• Length = 23 m
• Breadth = 11 m

Answer 2

Answer:

Length= 23 m

Breadth=11 m

Step-by-step explanation:

Hope you find this helpful............