Chapter 10, Problem 1E

To determine

To find: perimeter of the triangle.

Answer to Problem 1E

The perimeter of the triangle is29.2 units

Explanation of Solution

Given:

  

1. 26.7 units
2. 29.2 units
3. 34.5 units
4. 48.6 units

Formula used:

The distance d between these points is calculated as

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

Calculation:

  

Observe the positions of the coordinates and find out the coordinates of each point of the triangle.

For example, point X is 4 unit of the left of origin and 5 units upwards. Hence its coordinates will be (-4,5)

Similarly, Y (3.2) and Z (-4, -6)

The coordinates are X (-4,5), Y (3,2) & Z (-4, -6) Apply distance formula by keeping the values of the two coordinates

Hence

For Side XY

  $d=\sqrt{{\left(2-5\right)}^2+{(3-(-4))}^2}$

Or, $d=\sqrt{{\left(-3\right)}^2+{(7)}^2}$

Or, $d=\sqrt{9+49}$

Or, $d=\pm \sqrt{58}$ (distance can’t be negative so omit the negative root found)

Or, $d=7.6$

Similarly, for side YZ

  $d=\sqrt{{\left(2-\left(6\right)\right)}^2+{(3-(-4))}^2}$

Or, $d=\sqrt{{\left(8\right)}^2+{(-7)}^2}$

Or, $d=\sqrt{64+49}$

Or, $d=\pm \sqrt{113}$

Or, $d=\sqrt{113}$ (distance can’t be negative so omit the negative root found)

Or, $d=10.6$

Lastly for side ZX

  $d=\sqrt{{\left(5-\left(-6\right)\right)}^2+{\left(\left(-4\right)-\left(-4\right)\right)}^2}$

Or, $d=11$ (distance can’t be negative so omit the negative root found)

Hence the measure of all the three sides is

  $\begin{array}{l}XY=\sqrt{58}=7.6\\ YZ=\sqrt{113}=10.6\\ ZX=11\end{array}$

Thus perimeter (P) $=XY+YZ+ZX$

  $P=7.6+10.6+11$

  $P=29.2\text{ units}$

Conclusion:

Hence, option B is the correct one.