Question

The length of a rectangle is three meter more than its width. If both length and breadth are decreased by 2 centimeter, then the area is reduced by 18 square units. Find the dimensions of the rectangle. Then I will follow and mark as branliest​

Answer 1

Answer:

Length of Rectangle be (X + 3)m

Width of Rectangle be X

Area of Rectangle = L×B

=(X+3) × X m^2

New Area

1m = 100cm

1cm = (1 /100) m

2cm = (1 / 100) × 2 = 0.02 m

(X+3)-0.02 × (X - 0.02) = 18

(0.02X + 0.06) (X - 0.02) = 18

0.02X^2 + 0.02X × 0.02 + 0.06 × X - 0.06× 0.02 = 18

0.02X^2 + 0.0004X + 0.0036X - 0.0012 = 18

0.02X^2 + 0.0040X - 0.0012 - 18 = 0

0.02X^2 + 0.0040X - 0.0030 = 0

Divided whole thing by 0.02

X^2 + 0.2X - 0.15 = 0

X^2 + 0.5X - 0.3X - 0.15 = 0

X ( X + 0.5 ) - 0.3 ( X + 0.5 ) = 0

(X - 0.3) ( X + 0.5 ) = 0

X = 0.3 meter

Therefore

Dimensions of Rectangle

Lenght = X + 3 = 0.3 + 3 = 3.3 meter

Width = X = 0.3 meter

Answer 2

●GIVEN :

• LENGTH OF A RECTANGLE IS 3 METER MORE THAN ITS WIDTH

• IF BOTH LENGTH AND BREADTH ARE DECREASED BY TWO METER THEN AREA IS REDUCED BY 18 sq.units

●TO FIND :

• DIMENSIONS OF RECTANGLE

●SOLUTION :

○CASE - I :

LET THE WIDTH OF RECTANGLE BE X cm

THEN LENGTH = X + 3 cm

AREA OF RECTANGLE = L × B = X ( X + 3) = X^2 + 3X sq.cm

○CASE - II :

LENGTH = X + 3 - 2 = X + 1 cm

BREADTH = X - 2 cm

AREA = X^2 + 3X - 18 sq.cm

=> L × B = X^2 + 3X - 18

=> (X + 1 )( X - 2) = X^2 + 3X - 18

=> X^2 - 2X + X - 2 = X^2 + 3X - 18

=> -2 - X = 3X - 18

=> 0 = 4X - 16

=> 4X = 16 => X = 4

THEN ,

BREADTH = (X) = 4 cm

LENGTH = ( X + 3) = 7 cm

∴ THE DIMENSIONS OF THE RECTANGLE ARE 4 cm & 7cm

HOPE IT HELPS !!!!