Question

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?)

Answer 1

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