Question

The area of a rectangle gets increased by 30 square units, if its length is reduced by 3 units and
breadth is increased by 5 units. If we increase the length by 5 units and reduce the breadth by
3 units then the area of a rectangle reduces by 10 square units. Find the length and breadth of
the rectangle.​

Answer 1

Answer:

let length is x unit and breadth is y unit

then area is xy

again, (x-3)(y+5)-30=xy

xy-3y+5x-15-30=xy

5x-3y=45

15x-9y=135

agai n,

(x+5)(y-3)+10=xy

xy+5y-3x -15+10=xy

-3x+5y=5

-15x+25y=25

adding,

16y=160

y=160/16=10

5x-3y=45

5x-3.10=45

5x=45+30=75

x=75/5=15

so length of the rectangle is 15 unit and breadth of the rectangle is 10 unit

Answer 2

Answer:

step by step explanation

let length of rectangle be x and breath of rectangle be y.

According to given condition,

(x-3)(y+5) =30 + xy

xy+5x-3y-15-30=xy

xy will be cut by xy , so we get

5x-3y-45=0 ..........(1)

then, (x+5)(y-3)+10=xy

xy+5y-3x-15+10=xy

again xy and xy will be cutted, so we get

-3x+5y=5........(2)

multiplying eq 1 by 3 and eq 2 by 5 and then solving it by elinmination method, we get

-15x+25y=25

15x-9y =135. here -15 and 15 willcut

—--———-—-—

16y=160

y=160/16

y=10

putting value of y in eq 1. ( You can put value of y in any eq as you wish).

5x-3y=45

5x-3(10)=45

5x-30=45

5x=45+30

5x=75

x=75/5

x=15

Thank you hope you can understand .