# The width of the rectangle is half its length. If the width is increased by 3 cm and the length by 2 cm

The width of the rectangle is half its length. If the width is increased by 3 cm and the length by 2 cm, then its area will increase by 78 cm (2). Find the length and width of the rectangle.

1. Let’s designate the width of the rectangle “X”. Then its length will be “2X”. Let’s write the expression for the area of this rectangle:

S = 2X * X = 2X ^ 2.

2. If the width is increased by 3 cm, the new width will be “X + 3”. The length was increased by 2 cm, so the new length will be “2X + 2”.

The area will increase by 78 cm ^ 2, hence it will be “2X ^ 2 + 78”. Let’s write the equation and solve it:

(2X + 2) * (X + 3) = 2X ^ 2 + 78;

2X ^ 2 + 2X + 6X + 6 = 2X ^ 2 + 78;

8X = 72;

X = 72/8;

X = 9 (cm) is the width.

3. Find the length:

9 * 2 = 18 (cm).

Answer: the length of the rectangle is 18 cm and the width is 9 cm.

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