Find the missing side lengths, perimeter, and area of triangle ABC on the coordinate plane. All answers should be in simplest radical form, if necessary.:
Side Length AB: Response area
Side Length BC: Response area
Side Length AC: Response area
Perimeter of Triangle ABC: Response area
Area of Triangle ABC: Response area
Note: the formula for area of a triangle is A=bh2
, where b is the length of the base (BC) and h is the height from side BC to point A.
The option "square root of 5" (5 of 9) has been selected. Press tab to choose a response area, and spacebar to insert it.
2√2
2
3
5
√3
√5
√8
3+2√2+5√
7+√8
It seems that you are expecting instructions to complete an online form or interactive question, but there are a few problems with the information provided. You've mentioned triangle ABC on a coordinate plane, but without the coordinates of the vertices (A, B, and C), we cannot accurately calculate the side lengths or properties of the triangle like its perimeter or area.
Moreover, the formula given for the area of a triangle A = bh/2 is incomplete in your message; it should not end with bh2. The formula means that the area (A) is equal to one-half the base (b) times the height (h).
Additionally, you've indicated that the "square root of 5" (sqrt(5)) has been selected for something, but without context, it's unclear how this fits into the problem.
Here is how you could solve the problem given the proper coordinates:
1. If you have the coordinates of points A, B, and C, you can use the distance formula to find the lengths of sides AB, BC, and AC. The distance formula is:
Distance between two points (x1,y1) and (x2,y2) on a plane:
d = √((x2-x1)^2 + (y2-y1)^2)
2. To find the perimeter of the triangle, simply sum the lengths of the sides:
Perimeter = AB + BC + AC
3. If you have the base and height for the triangle, you can use the area formula mentioned above (with the correct version):
Area = (Base * Height) / 2
If the height is not perpendicular to the base in the provided coordinates, you would have to find a perpendicular height to calculate the area.
Please provide the coordinates of the vertices A, B, and C if you need a specific calculation, or if you want to insert a provided option into the "Response area," please provide clearer instructions or context for the task.