Question

DF =24, BC = 6, and DB = 8. Find the perimeter of ADF

Answer 1

The perimeter of ADF is 38 units.

Step-by-step explanation:

To find the perimeter of ADF, we need to add up the lengths of all the sides:

Adding these lengths together, we get the perimeter of ADF as 6 + 8 + 24 = 38 units.

Answer 2

Given BC as the segment at the midpoint, DF is found to be 12. The perimeter of
`ADF` is twice the perimeter of
`BCD`, resulting in a perimeter of 52 units.

Let's go through the problem step by step:

- BC is the segment at the midpoint of the triangle
`ADF`.

- BC = 6

- DB = 8

- DC is half of DF

1. Find DF:

-
`\(DC = (1)/(2) * DF\)`

- Substitute DC = 6:

`\[ 6 = (1)/(2) * DF \]`

DF = 12

2. Calculate AD:

- Since BC is the segment at midpoint,
`\(AD = 2 * BC\)`

- Substitute BC = 6:

`\[ AD = 2 * 6 = 12 \]`

3. Now as of the last step let us finally calculate the perimeter of triangle ADF. Since we know that we can determine the perimeter of the full triangle if you know the perimeter of the triangle formed by its mid-segments. The perimeter of the full triangle is twice the perimeter of the triangle formed by its mid-segments.

This is a consequence of the fact that mid-segments divide a triangle into smaller, similar triangles, and the ratio of corresponding sides in similar triangles is constant.

By this justification, the perimeter of ADF will be 2 times the perimeter of BCD.

Perimeter of ADF = 2 × (12+8+6)

= 2 × 26

= 52 units

The complete question is

In a triangle, DF =24, BC = 6, and DB = 8. Find the perimeter of
`ADF`. (image attached)