Question

A triangle has vertices at (-4,-6),(3,3), (7,2). Rounded to two decimal places, which of the following is the closest approximation of

the perimeter of the triangle?

A. 19.34
B. 12.36
C. 15.52
D. 29.12

Answer 1

The perimeter of the triangle is found by calculating the distance between each pair of vertices and summing them up, resulting in an approximate perimeter of 29.12 when rounded to two decimal places.

Step-by-step explanation:

To find the closest approximation of the perimeter of the triangle with vertices at (-4,-6), (3,3), and (7,2), first, we need to calculate the distances between these points using the distance formula, which is √[(x2-x1)2 + (y2-y1)2].

Distance between (-4,-6) and (3,3) is √[(3 - (-4))2 + (3 - (-6))2] = √[72 + 92] = √[130]

Distance between (3,3) and (7,2) is √[(7 - 3)2 + (2 - 3)2] = √[42 + (-1)2] = √[17]

Distance between (7,2) and (-4,-6) is √[(7 - (-4))2 + (2 - (-6))2] = √[112 + 82] = √[185]

Next, we add these distances together to compute the perimeter:

√[130] + √[17] + √[185] ≈ 11.40 + 4.12 + 13.60 = 29.12

Therefore, the closest approximation of the triangle's perimeter, rounded to two decimal places, is 29.12.

The correct option is D. 29.12.

Answer 2

Hey there!

The perimeter of the triangle is the distance around it.

We can find the distance of two points using the distance formula, and add up all the distances to find the total distance.

-4, -6 to 3, 3 is 2

3, 3 to 7, 2 is 5

7, 2 to -4, -6 is about 5.4

2+5+5.39=12.4, which is closest to 12.36.

Let me know if this helps :)