Chapter 1, Problem 21PT

To determine

To calculate the perimeter of the polygon

Answer to Problem 21PT

38 units

Explanation of Solution

Given information:

Vertices of the rectangle

  $P(0,0),Q(0,7),R(12,7),\text{}S(12,0)$

Formula used:

Distance= $\sqrt{{\left(x_2^{}-x_1^{}\right)}^2+{\left(y_2^{}-y_1^{}\right)}^2}$

Calculation: calculate distance between PQ, QR, RS, SP using distance formula and then add all of these

Distance between PQ

Distance = $\sqrt{{\left(0-0\right)}^2+{\left(7-0\right)}^2}$

Solving it further

Distance = $\sqrt{49}$

Solving it further

PQ= 7 units

Now, distance between QR

Distance = $\sqrt{{\left(12-0\right)}^2+{\left(7-7\right)}^2}$

Solving it further

QR= $\sqrt{144}$

Solving it further

QR = 12 units

Now, distance between RS

Distance = $\sqrt{{\left(12-12\right)}^2+{\left(0-7\right)}^2}$

Solving it further

RS= $\sqrt{49}$

Solving it further

RS= 7 units

Now, distance between SP

Distance = $\sqrt{{\left(0-12\right)}^2+{\left(0-0\right)}^2}$

Solving it further

SP= $\sqrt{144}$

Calculating the distance

SP= 12 units

Final perimeter

  Perimeter= $PQ+QR+RS+SP$

Substituting values

  Perimeter= $7+12+7+12$

The final answer is

38 units