Question

if the length of rectangle is increased by 10 cm and the breadth is decreased by 5cm the area remain unchanged .if the length is decreased by 5cm and length is increased by 4 cm,even then its area remain unchanged .find the dimensions of the rectangle.

Answer 1

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Answer 2

Answer:

The dimensions of rectangle is x=30 and y=20.

Step-by-step explanation:

Given : If the length of rectangle is increased by 10 cm and the breadth is decreased by 5cm the area remain unchanged .if the length is decreased by 5cm and length is increased by 4 cm,even then its area remain unchanged .

To find : The dimensions of the rectangle.

Solution : Let x be the length

Let y be the breadth.

Area of rectangle is $A=L\times B$

$A=x\times y=xy$

If the length of rectangle is increased by 10 cm and the breadth is decreased by 5 cm the area remain unchanged

Length = x+10

Breadth = y-5

Area remain unchanged

$A=(x+10)\times (y-5)$

$xy=(x+10)\times (y-5)$

$xy=xy-5x+10y-50$

$-5x+10y=50$

$-x+2y=10$  ........[1]

If the length is decreased by 5cm and length is increased by 4 cm,even then its area remain unchanged .

$A=(x-5)\times (y+4)$

$xy=(x-5)\times (y+4)$

$xy=xy+4x-5y-20$

$4x-5y=20$ ..........[2]

Solving equation [1] and [2]

Multiply [1] with 4 and add in [2]

$-4x+8y+4x-5y=40+20$

$3y=60$

$y=20$

Put value of y in [1]

$-x+2y=10$

$-x+2(20)=10$

$-x+40=10$

$x=30$

The dimensions of rectangle is x=30 and y=20.