# Find the Length and Width of the Rectangle ?

If one side of a square is doubled in length and the adjacent side is decreased by four centimeters, then the area of the resulting rectangle is 48 square centimeters larger than that of the original square. Find the length and width of the rectangle.

1. 12 cm, 8 cm
2. 11cm, 9 cm
3. 24 cm 8 cm
4. 24 cm, 12 cm

Answer: (3) 24 cm, 8 cm

Explanation:-
Let the side of a square be X meters.
Then, the area of a square = X² meters

One side of a square is doubled in length and the adjacent side is decreased by 4 cm.
Then, the length of a new rectangle = 2 X cm and the width of a new rectangle = (X – 4) cm

Therefore, the area of a new rectangle = 2 X . (X – 4)
= 2 X² – 2 x 4 X
= (2 X² – 8 X) cm square

Then, the area of the resulting rectangle is 48 square centimeters larger than that of the original square.

So, (2 X² – 8 X) – X² = 48
2 X² – 8 X – X² = 48
X² – 8 X – 48 = 0
X² – 12 X + 4 X – 48 = 0
X (X – 12) + 4( X – 12) = 0
(X + 4) (X – 12)= 0
X – 12 = 0
X = 12

Then, the length of the new rectangle = 2 x 12
= 24 cm
And, the width of the new rectangle = 12 – 4
= 8 cm

Hence, the answer is (3) 24 cm, 8 cm.