Answer:
The total perimeter of the triangle, rounded to the nearest tenth, is 37.5 units.
Step-by-step explanation:
You can answer this simply by applying the Pythagorean theorem to each side, finding each side's length and then adding them up.
The top side goes from -8x7 to 6x3, so so the change on the x axis is 6 - (-8), or 14, and on the y axis it's 7 - 3, or 4.
That means that the top side has a length of:
[tex]\sqrt{14^2 + 4^2} \\= \sqrt{196 + 16}\\= \sqrt{212}\\\approx 14.6[/tex]
Similarly with the right side, we have a Δy of 7 and a Δx of 4:
[tex]\sqrt(7^2 + 4^2)\\= \sqrt(49 + 16)\\= \sqrt(65)\\\\\approx 8.1[/tex]
And with the remaining side:
[tex]\sqrt{10^2 + 11^2}\\= \sqrt{100 + 121}\\= \sqrt{221}\\\approx 14.9\\[/tex]
Now we can just sum up those three numbers to get the approximate perimeter:
14.6 + 14.9 + 8.1
= 29.5 + 8.1
= 37.6
Now that matches none of the answers given, but is very close to answer C. The difference here happens because of where rounding is done. I rounded to the nearest tenth on every side length, but they rounded on the end result.
