Question
AB has length 19 cm, BC has length 29 cm, and CD has length 13 cm. What is the length of the diameter, ED, if the radius is AD
Answers
GPT 3.5
First, we need to find the length of the radius AD.
By triangle inequality,
AD < AB + BC
AD < 19 + 29
AD < 48
Next, we need to find the length of DE.
DE = AB - CD
DE = 19 - 13
DE = 6 cm
Now, we can use Pythagoras theorem to find the length of AD.
AD^2 = DE^2 + CD^2
AD^2 = 6^2 + 13^2
AD^2 = 36 + 169
AD^2 = 205
AD ≈ 14.32 cm
Since the radius is AD, the diameter ED will be twice the length of the radius.
ED = 2 * AD
ED = 2 * 14.32
ED ≈ 28.64 cm
Therefore, the length of the diameter, ED, is approximately 28.64 cm.
By triangle inequality,
AD < AB + BC
AD < 19 + 29
AD < 48
Next, we need to find the length of DE.
DE = AB - CD
DE = 19 - 13
DE = 6 cm
Now, we can use Pythagoras theorem to find the length of AD.
AD^2 = DE^2 + CD^2
AD^2 = 6^2 + 13^2
AD^2 = 36 + 169
AD^2 = 205
AD ≈ 14.32 cm
Since the radius is AD, the diameter ED will be twice the length of the radius.
ED = 2 * AD
ED = 2 * 14.32
ED ≈ 28.64 cm
Therefore, the length of the diameter, ED, is approximately 28.64 cm.