What is the length of the altitude from vertex A to side BC in triangle ABC with
Practice Questions
Q1
What is the length of the altitude from vertex A to side BC in triangle ABC with sides 5 cm, 12 cm, and 13 cm?
5 cm
6 cm
12 cm
13 cm
Questions & Step-by-Step Solutions
What is the length of the altitude from vertex A to side BC in triangle ABC with sides 5 cm, 12 cm, and 13 cm?
Step 1: Identify the sides of triangle ABC. The sides are 5 cm, 12 cm, and 13 cm.
Step 2: Determine if the triangle is a right triangle. Since 5² + 12² = 13² (25 + 144 = 169), it is a right triangle.
Step 3: In a right triangle, the area can be calculated using the formula: Area = (1/2) * base * height. Here, we can use the two shorter sides (5 cm and 12 cm) as the base and height.
Step 4: Calculate the area of the triangle: Area = (1/2) * 5 * 12 = 30 cm².
Step 5: Now, we need to find the altitude (height) from vertex A to side BC. We can use the area formula again: Area = (1/2) * base * height, where the base is side BC (which is 12 cm).
Step 6: Set up the equation using the area we found: 30 cm² = (1/2) * 12 * height.
Step 7: Solve for height: 30 = 6 * height, so height = 30 / 6 = 5 cm.
