Question

The area of 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 units the area will increase by 50 square units find the length and breadth of the rectangle

Answer 1

Answer:

Length = 40

Breadth = 30

Step-by-step explanation:

Given: As in first case

• Area of rectangle gets reduced by 80 sq units
• Its Length and Breadth reduced by 5 sq units and increased by 2 sq units respectively

★In second case

• Its length is increased by 10 sq units and Breadth is decreased by 5 sq units.
• Then, Area of rectangle will increase by 50 sq units.

To find: Length and Breadth of rectangle

Solution: Let Length be 'x' and Breadth be 'y'.

Then, Area of rectangle will be Length x Breadth = xy

According to the question : In Case (1)

$\large\implies{\sf }$ ( x–5)(y+2)=xy – 80

$\large\implies{\sf }$ x(y+2) –5(y+2) = xy –80

$\large\implies{\sf }$ xy + 2x – 5y –10 = xy –80

$\large\implies{\sf }$ 2x – 5y –10 = –80

$\large\implies{\sf }$ 2x – 5y = –80 + 10

$\large\implies{\sf }$ 2x – 5y = –70 .................. ( equation 1)

→ In second case

$\large\implies{\sf }$ (x+10)(y–5) = xy + 50

$\large\implies{\sf }$ x(y–5) +10(y–5) = xy + 50

$\large\implies{\sf }$ xy –5x + 10y –50 = xy + 50

$\large\implies{\sf }$ –5x + 10y = 50 + 50

$\large\implies{\sf }$ –5x + 10y = 100 ................. ( equation 2)

Now, Multiplying both sides of equation 1 by 2

=> 2(2x–5y) = 2(–70)

=> 4x – 10y = –140

Solving both equations ( eqn 1 and eqn 2)

=> –5x + 10y = 100

⠀⠀⠀4x – 10y = –140

__________________________

⠀⠀⠀–x = –40

or x = 40

Hence, We get Breadth of rectangle 'x' = 40 units

Now, Putting the value of 'x' in equation 2nd We got:

$\large\implies{\sf }$ –5 x 40 + 10y = 100

$\large\implies{\sf }$ –200 + 10y = 100

$\large\implies{\sf }$ 10y = 100+200

$\large\implies{\sf }$ 10y = 300

$\large\implies{\sf }$ y = 30 units

Hence, We get Length of rectangle 'y' = 30 units.

Answer 2

Answer:

Length= 40 units

Breadth= 30 units

Step-by-step explanation:

$\huge\underline\purple{\sf Given :-}$

• Area of rectangle will reduce by 80 units if its length is reduced by 5 units and Breadth is increased by 2 units.

• Area of rectangle will increase by 50 units if it's length is increased by 10 units and Breadth is decreased by 5 units.

To find: Length and Breadth of Rectangle

Solution: Let length and breadth be x and y respectively.

A/q ,

→ xy– 80 = (x–5)(y+2)

→xy–80 = x(y+2) – 5 (y+2)

→xy –80 = xy + 2x –5y –10

→ –80+10 = 2x – 5y

→ –70 = 2x – 56 ............(1)

† In second case † A/q

→(x-10)(y–5) = xy + 50

→x(y–5)+10(y–5) = xy + 50

→xy–5x+10y–50 = xy + 50

→ –5x + 10y = 50+50

→ –5x + 10y = 100.............(2)

Multiplying equation (1) by 5 and equation (2) by 2 , We get

10x–25y=–350

–10x +25y= 200

_____________________

–5y =. –150

So, Y = 150/5 = 30

Hence, Breadth of rectangle = y = 30 units

Putting value of Y in equation (1) we get,

→2x–5y = –70

→2x = –70 + 5 x 30

→2x = 80

→x = 80/2 = 40 units

Hence, Length of rectangle = x = 40 units