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

# The area of a rectangle gets reduced by 80 square units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 square units. Find the length and breadth of the rectangle respectively.

1. A
40 units and 30 units
2. B
40 units and 50 units
3. C
50 units and 50 units
4. D
60 units and 50 units

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

Given the area of rectangle gets reduced by 80 sq. units if its length is decreased by 5 units and breadth is increased by 2 units.
If there is an increment in the length by 10 units and decrement in the breadth by 5 units, then area is increased by 50 square units.
Let the length and breadth of rectangle be x and y respectively.
We know the area of a rectangle is given by,
$A=\mathit{length}×\mathit{breadth}$
So, here we have,
Area = $x×y=\mathit{xy}$
According to the question, we have,

Similarly, from the second condition,

The solution of the equations by cross multiplication method is given by the formula,
$\frac{x}{{b}_{1}{c}_{2}-{b}_{2}{c}_{1}}=\frac{y}{{a}_{2}{c}_{1}-{a}_{1}{c}_{2}}=\frac{1}{{a}_{1}{b}_{2}-{a}_{2}{b}_{1}}$
Here,
Using the cross-multiplication method to find the value of x and y,
$⇒\frac{x}{-5\left(20\right)-70\left(-2\right)}=\frac{y}{70\left(1\right)-\left(20\right)2}=\frac{1}{2\left(-2\right)-\left(1\right)\left(-5\right)}$
$⇒\frac{x}{40}=\frac{y}{30}=\frac{1}{1}$

$⇒y=\frac{30}{1}=30$
Therefore, the length and breadth of the rectangle are 40 units and 30 units respectively.
Hence, option (1) is correct.

## Related content

 Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)