Question

shea drew the rectangle reduction.
18.6 mm
31 mm
3 mm
figures not drawn to scale.
what is the perimeter, in millimeters, of the reduced rectangle?
8
16
49.6
99.2

Explanation:

Step1: Find the scale factor

The scale factor \(k\) is found by comparing the corresponding sides of the two rectangles. Let's assume the side of length \(18.6\) mm in the original rectangle corresponds to the side of length \(3\) mm in the reduced rectangle.
\(k=\frac{3}{18.6}=\frac{30}{186}=\frac{5}{31}\)

Step2: Find the length of the other side of the reduced rectangle

Let the other side of the original rectangle be \(l = 31\) mm. Using the scale factor \(k\), the length of the other side of the reduced rectangle \(l_{new}=31\times k\)
\(l_{new}=31\times\frac{5}{31} = 5\) mm

Step3: Calculate the perimeter of the reduced rectangle

The formula for the perimeter of a rectangle is \(P = 2(a + b)\), where \(a\) and \(b\) are the sides of the rectangle. Here \(a = 3\) mm and \(b=5\) mm
\(P=2(3 + 5)\)
\(P=2\times8\)
\(P = 16\) mm

Answer:

16