The length of the rectangle exceeds its breadth by 3 cm. if the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. find the length and breadth of the given rectangle.

Let's suppose the breadth of the rectangle be x cm 

The length of the rectangle = x + 3 cm

It is assumed that the length and breadth of the rectangle is amplified by 2.

Now, the breadth of the rectangle = x + 2

The length of the rectangle = x + 3 + 2 = x + 5

It is also assumed that the area of the rectangle is 70 sq. cm

Hence, the area of the rectangle = length x breadth = (x + 2)(x + 5) = 70

= x2 + 5x + 2x + 10 = 70

= x2 + 7x = 70 - 10

=  x2 + 7x = 60

= x2 + 7x - 60 = 0

= x2 + 12x - 5x - 60 = 0

=  x( x + 12) -5(x + 12) = 0

= ( x + 12) (x - 5) = 0

=x + 12 = 10               or              =x - 5 = 0

= x = 10 - 12 = -2               = x = 5

The breadth of a rectangle is never negative, so the value of x is 5 cm

Therefore, the breadth of the rectangle = 5 cm

The length of the rectangle = 5 + 3 = 8 cm

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

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