Question

The area of the rectangle reduce by nine sq units if its length is reduce by unit and breadth is increase in length by 3units and breadth by two units the area increased by 67 sq units find the dimension of the rectangle

Answer 1

Answer

Original question ,

The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and the breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Find the length and breadth of the rectangle.

Given,

• Area is reduced by 9sq units if the length is reduced by 5 unit and breadth is increased by 3 units.

• Area is increased by 67sq units if length is increased by 3 units and breadth is increased by 2 units.

To find,

• Dimensions of the rectangle

Solution ,

Let the length of the rectangle be : x units

Let the length of the rectangle be : x unitsLet the breadth of the rectangle be : y units

We know that area of rectangle is :

length × breadth

Area = xy

If length is reduced by 5 units and the breadth is increases by 3 units, then area is reduced by 9 sq. units.

∴ (x − 5)(y + 3) = xy − 9

⇛ xy + 3x −5y − 15 = xy − 9

⇛ 3x − 5y − 6 = 0 ------------(1)

If length is increased by 3 units and breadth by 2 units, the area is increased by 67 sq. units.

∴ (x + 3)(y + 2) = xy + 67

⇛ xy + 2x + 3y + 6 = xy + 67

⇛ 2x + 3y − 61 = 0 -----------(2)

Thus, we get the following system of linear equations:

• 3x − 5y − 6 = 0
• 2x + 3y − 61 = 0

Let us solve it by elimination method.

Multiply equation (1) by 3

Multiply equation (2) by 5

We get :

• 9x - 15y - 18 = 0 -----------(3)
• 10x + 15y - 305 = 0 ----------(4)

Adding (3) & (4) We get,

⇛ 19x - 323 = 0

⇛ $\rm x = \frac { 323 } { 19 }$

⇛ x = 17

Putting x = 17 in equation (1)

We get,

⇛ 3(17) - 5y - 6 = 0

⇛ 51 - 5y - 6 = 0

⇛ 45 = 5y

⇛ y = 9

Hence we got:

• Length = 17 units
• Breadth = 9 units

Answer 2

Answer:

l=17 b=9

Step-by-step explanation:

pls make it brainlest answer