Question

part b
calculate the perimeter of the figure from part a.

Explanation:

Step1: Identify the points

The points of the triangle are (0,3), (0,0) and (5,0).

Step2: Calculate side - lengths

The length between (0,3) and (0,0) is $d_1=\sqrt{(0 - 0)^2+(3 - 0)^2}=3$.
The length between (0,0) and (5,0) is $d_2=\sqrt{(5 - 0)^2+(0 - 0)^2}=5$.
The length between (0,3) and (5,0) is $d_3=\sqrt{(5 - 0)^2+(0 - 3)^2}=\sqrt{25 + 9}=\sqrt{34}$.

Step3: Calculate perimeter

The perimeter $P=d_1 + d_2 + d_3=3+5+\sqrt{34}=8+\sqrt{34}$.

Answer:

$8+\sqrt{34}$