The lengths of line segments AB and BD are in a 2:3 ratio. The length of line segment AD is given as 20. By setting AB = 2x and BD = 3x, where x is the common factor, and using the equation AD = AB + BD, the value of x is found to be 4. Therefore, the lengths of AB and BD are 8 and 12 respectively.

1. The lengths of line segments 𝐴𝐵 and 𝐵𝐷 are in ratio 2:3. If the length of line segment
𝐴𝐷 is 20, find the lengths of 𝐴𝐵 and 𝐵𝐷.
A B
D

2. The lengths of line segments 𝐴𝐵 and 𝐵𝐷 are in ratio 2:3. If the length of line segment
𝐴𝐷 is 20, find the lengths of 𝐴𝐵 and 𝐵𝐷.
A B
D
We think about a ratio as a simplified fraction.
So if AB/BD can be simplified to 2/3 so we can say
that 𝐴𝐵 = 2𝑥 and 𝐵𝐷 = 3𝑥 where 𝑥 is the
greatest common factor that was cancelled when
the ratio was simplified.

3. The lengths of line segments 𝐴𝐵 and 𝐵𝐷 are in ratio 2:3. If the length of line segment
𝐴𝐷 is 20, find the lengths of 𝐴𝐵 and 𝐵𝐷.
A B
D
We think about a ratio as a simplified fraction.
So if AB/BD can be simplified to 2/3 so we can say
that 𝐴𝐵 = 2𝑥 and 𝐵𝐷 = 3𝑥 where 𝑥 is the
greatest common factor that was cancelled when
the ratio was simplified.
We can use the segment-addition postulate to
express 𝐴𝐷 in terms of 𝐴𝐵 and 𝐵𝐷:
𝐴𝐷 = 𝐴𝐵 + 𝐵𝐷

4. The lengths of line segments 𝐴𝐵 and 𝐵𝐷 are in ratio 2:3. If the length of line segment
𝐴𝐷 is 20, find the lengths of 𝐴𝐵 and 𝐵𝐷.
A B
D
We think about a ratio as a simplified fraction.
So if AB/BD can be simplified to 2/3 so we can say
that 𝐴𝐵 = 2𝑥 and 𝐵𝐷 = 3𝑥 where 𝑥 is the
greatest common factor that was cancelled when
the ratio was simplified.
We can use the segment-addition postulate to
express 𝐴𝐷 in terms of 𝐴𝐵 and 𝐵𝐷:
𝐴𝐷 = 𝐴𝐵 + 𝐵𝐷
20 = 2𝑥 + 3𝑥 Substitute for the lengths of the segments.

5. The lengths of line segments 𝐴𝐵 and 𝐵𝐷 are in ratio 2:3. If the length of line segment
𝐴𝐷 is 20, find the lengths of 𝐴𝐵 and 𝐵𝐷.
A B
D
We think about a ratio as a simplified fraction.
So if AB/BD can be simplified to 2/3 so we can say
that 𝐴𝐵 = 2𝑥 and 𝐵𝐷 = 3𝑥 where 𝑥 is the
greatest common factor that was cancelled when
the ratio was simplified.
We can use the segment-addition postulate to
express 𝐴𝐷 in terms of 𝐴𝐵 and 𝐵𝐷:
𝐴𝐷 = 𝐴𝐵 + 𝐵𝐷
20 = 2𝑥 + 3𝑥
20 = 5𝑥
𝑥 = 4 Solve for 𝑥.

6. The lengths of line segments 𝐴𝐵 and 𝐵𝐷 are in ratio 2:3. If the length of line segment
𝐴𝐷 is 20, find the lengths of 𝐴𝐵 and 𝐵𝐷.
A B
D
We think about a ratio as a simplified fraction.
So if AB/BD can be simplified to 2/3 so we can say
that 𝐴𝐵 = 2𝑥 and 𝐵𝐷 = 3𝑥 where 𝑥 is the
greatest common factor that was cancelled when
the ratio was simplified.
We can use the segment-addition postulate to
express 𝐴𝐷 in terms of 𝐴𝐵 and 𝐵𝐷:
𝐴𝐷 = 𝐴𝐵 + 𝐵𝐷
20 = 2𝑥 + 3𝑥
20 = 5𝑥
𝑥 = 4
𝐴𝐵 = 2 ⋅ 4 = 8 and 𝐵𝐷 = 3 ⋅ 4 = 12 Substitute back in to get 𝐴𝐵 and 𝐵𝐷.