Question

What is the perimeter of each of the following figures? What do you infer from the answers?

Answer 1

Step 1: Determine the perimeter of figure (a).

Figure (a) is a square with the length of the side equal to.$25\mathrm{cm}$

Use the formula $P=4a$ to determine the perimeter:

$\begin{array}{rcl}P& =& 4\times 25\mathrm{cm}\\ \therefore P& =& 100\mathrm{cm}\end{array}$

Hence, the perimeter of the square in figure (a) is $100\mathrm{cm}$

Step 2: Determine the perimeter of figure (b).

Figure (b) is a rectangle with length and width equal to $20\mathrm{cm}$ and $30\mathrm{cm}$respectively.

Use the formula $P=2\left(l+w\right)$ to determine the perimeter:

$$\begin{gathered} \begin{array}{rcl}P& =& 2\left(20+30\right)\mathrm{cm}\\ & \Rightarrow & P=2\times 50\mathrm{cm}\end{array} \\ \begin{array}{rcl}& \Rightarrow & P=100\mathrm{cm}\end{array} \end{gathered}$$

Hence, the perimeter of the rectangle in figure (b) is$100\mathrm{cm}$.

Step 3: Determine the perimeter of figure (c).

Figure (c) is also a rectangle with length and width equal to 10 cm and 40 cm respectively.

Use the formula $P=2\left(l+w\right)$ to determine the perimeter:

$$\begin{gathered} \begin{array}{rcl}P& =& 2\left(10+40\right)\mathrm{cm}\\ & \Rightarrow & P=2\times 50\mathrm{cm}\end{array} \\ \begin{array}{rcl}& \Rightarrow & P=100\mathrm{cm}\end{array} \end{gathered}$$

Hence, the perimeter of the rectangle in figure (c) is$100\mathrm{cm}$.

Step 4: Determine the perimeter of figure (d).

Figure (d) is a triangle with the lengths of sides are equal to $30\mathrm{cm},30\mathrm{cm},\mathrm{and}40\mathrm{cm}$

Add the lengths of triangle to find the perimeter:

$\begin{array}{rcl}\mathrm{P}& =& 30\mathrm{cm}+30\mathrm{cm}+40\mathrm{cm}\\ & \Rightarrow & \mathrm{P}=100\mathrm{cm}\end{array}$

Hence, the perimeter of the triangle figure (d) is$100\mathrm{cm}$.

From the calculation of all parts, it can be stated that the perimeter of all the figures is equal.