Write and solve a system of equations to solve this problem. Explain why you choose the method you used. (The length of a rectangle is 3 times the width. The perimeter is 44 cm. What are the dimensions of the rectangle?)

We need to identify the given data.

Given:

Width is unknown but it is the basis of the measurement of length.

Width = x

Length = 3x

Perimeter = 44cm

Perimeter is solved by adding all the sides of the rectangle. In rectangles, opposite sides are equal.

Perimeter = Length + Length + Width + Width

or simply: Perimeter = 2 (Length+Width)

44cm = 2 (3x + x)

44cm = 2 (4x)

44cm = 8x

44cm/8 = 8x/8

5.5cm = x ⇒ width of the rectangle.

Since length is said to be three times the width, so ⇒ 3*5.5 = 16.5cm

Length = 16.5 cm

Width = 5.5 cm

To check: We use the Perimeter formula

P = 2 (l+w)

44cm = 2 (16.5cm + 5.5cm)

44cm = 2 (22cm)

44cm = 44cm