Answer:
The perimeter is 72 units and the area is 149 square units.
Step-by-step explanation:
[tex]\triangle SBA[/tex] has coordinates [tex]S(15,-8),B(-2,21)[/tex] and [tex]A(0,0)[/tex]
Using the distance formula.........
Length of side [tex]SB = \sqrt{(15+2)^2+(-8-21)^2}= \sqrt{17^2+(-29)^2}= \sqrt{1130}[/tex]
Length of side [tex]BA= \sqrt{(-2)^2+(21)^2}= \sqrt{445}[/tex]
Length of side [tex]AS =\sqrt{(15)^2+(-8)^2}=\sqrt{289}=17[/tex]
So, the perimeter of the triangle will be: [tex](SB+BA+AS)= \sqrt{1130}+ \sqrt{445}+17 =71.71... \approx 72[/tex] units. (Rounded to the nearest unit)
The height of the triangle for the corresponding base [tex]SB[/tex] is 8.89 units.
Formula for the Area of triangle, [tex]A= \frac{1}{2}(base\times height)[/tex]
So, the area of the [tex]\triangle SBA[/tex] will be: [tex]\frac{1}{2}(\sqrt{1130}\times 8.89)= 149.42... \approx 149[/tex] square units. (Rounded to the nearest unit)
