# The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 minutes and breadth is increased by 3 units if we increase the length by 3 units if we increase a length by three years and the breadth by 2 units the area increases 67 square then find the dimension of the rectangle. (By elimination method)

Given:

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units.

If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units.

To do:

We have to find the dimensions of the rectangle.

Solution:

Let the original length of the rectangle be $l$ and the breadth be $b$.

Area of the original rectangle $=lb$.

In the first case, the length is reduced by 5 units and breadth is increased by 3 units, the area of the rectangle is reduced by 9 square units.

New length $=l-5$

New breadth $=b+3$

The area formed by the new rectangle $=(l-5)(b+3)$ sq. units

According to the question,

$(l-5)(b+3)=lb-9$

$lb-5b+3l-15=lb-9$

$3l-5b=15-9$

$3l-5b=6$

$3l=6+5b$

$l=\frac{6+5b}{3}$.....(i)

In the second case, the length is increased by 3 units and breadth is increased by 2 units, the area is increased by 67 sq. units.

New length $=l+3$

New breadth $=b+2$

The area formed by the new rectangle $=(l+3)(b+2)$ sq. units

According to the question,

$(l+3)(b+2)=lb+67$

$lb+2l+3b+6=lb+67$

$2l+3b=67-6$

$2l+3b=61$.....(ii)

Substituting the value of $l=\frac{6+5b}{3}$ in (ii), we get,

$2(\frac{6+5b}{3})+3b=61$

Multiplying by $3$ on both sides, we get,

$3\times2(\frac{6+5b}{3})+3\times3b=3\times61$

$2(6+5b)+9b=183$

$12+10b+9b=183$

$19b=183-12$

$19b=171$

$b=\frac{171}{19}$

$b=9$

Substituting $b=9$ in equation (i), we get,

$l=\frac{6+5\times9}{3}$

$l=\frac{6+45}{3}$

$l=\frac{51}{3}$

$l=17$

The dimensions of the rectangle are $17$ units (length) and $9$ units (breadth).

Related Articles

- The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
- If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.
- In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.
- The length of a rectangle is greater than the breadth by 18cm. If both length and breadth are increased by 6 cm, then area increases by 168cm square. Find the length and breadth of the rectangle
- The area of a rectangle remains the same if the length is increased by 7 metres and the breadth is decreased by 3 metres. The area remains unaffected if the length is decreased by 7 metres and breadth is increased by 5 metres. Find the dimensions of the rectangle.
- The breadth of a rectangle is 4 cm less than its length if the length is increased by 4 cm and the breadth is decreased by 1 cm, the area of the rectangle is increased by $40\ cm^2$. Find the length and breadth of the rectangle.
- The length of a rectangle exceeds its width by 3 m. If the width is increased by 4 m and the length is decreased by 6 m, the area is decreased by 22 sq. m. Find the dimensions of the rectangle.
- ,p>If the length and breadth of a rectangle are doubled, by what percentage is it\'s area increased
- The length and breadth of a rectangle are in the ratio 5:3. If the perimeter is 80 cm, find the length and breadth of rectangle.
- The length of a rectangle is 80 m and the breadth is $\frac{3}{4}$ of its length. Find the area of the rectangle.
- The area of rectangle is 120 metre square and its breadth is 8 metre. Find the length of the rectangle and perimeter of the rectangle.
- The breadth of the rectangle is $\frac{3}{4}$th of its length and the perimeter of rectangle is 140 cm. Find the length and breadth of the rectangle.
- If each edge of a cube is increased by $50$ %, find the percentage increase surface area.
- Find the value of $a$ for which the area of the triangle formed by the points $A (a, 2a), B (-2, 6)$ and $C (3, 1)$ is 10 square units.
- Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.(ii) A fraction becomes $\frac{1}{3}$ when 1 is subtracted from the numerator and it becomes $\frac{1}{4}$ when 8 is added to its denominator. Find the fraction.(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

##### Kickstart Your Career

Get certified by completing the course

Get Started