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: (5 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Side Length AB: 5 Side Length BC: 5 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=bh2A=bh2, where b is the length of the base (BC) and h is the height from side BC to point A.

1 answer

To find the missing side lengths, perimeter, and area of triangle ABC, we need to use the given side lengths. You mentioned that sides AB and BC both have lengths of 5.

Step 1: Identify the lengths of the sides

  • Side Length AB: 5
  • Side Length BC: 5
  • Side Length AC:

For triangle ABC, since AB = BC, triangle ABC is isosceles. We can find the length of AC using the distance formula if we know the coordinates of points A, B, and C. However, since the coordinates aren't provided, we'll need more information to calculate AC.

Step 2: Calculate the perimeter

The perimeter \( P \) of triangle ABC can be calculated by adding the lengths of all sides: \[ P = AB + BC + AC \] Since AB and BC are both 5, if we denote the length of AC as \( x \): \[ P = 5 + 5 + x = 10 + x \]

Step 3: Calculate the area

To calculate the area \( A \) of triangle ABC, we can utilize the given formula with side BC as the base. However, we need the height \( h \) from point A to line segment BC.

The area can be expressed as: \[ A = \frac{1}{2} \times b \times h \] Where:

  • \( b \) is the length of side BC (which is 5)
  • \( h \) is the height from point A to line BC

Since we don't have coordinates for points A, B, or C, we cannot directly calculate \( h \). We would need additional information to find \( h \).

Summary of Values

  • Side Length AC:
  • Perimeter of Triangle ABC: \( 10 + x \)
  • Area of Triangle ABC:

Please provide the coordinates of points A, B, and C or additional information about side AC or the height \( h \) to find these values.