Question

In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE . If 10AB, 16BC , and 13AD then find the length of AE ?

Answer 1

In the given diagram, points B and D lie on sides AC and AE such that BD is parallel to CE. By using the concept of proportionality, we can find that the length of AE is approximately 12.31.

Step-by-step explanation:

In the given diagram, we have points B and D on sides AC and AE respectively, such that BD is parallel to CE. We are given that 10AB, 16BC, and 13AD. We need to find the length of AE.

Since BD is parallel to CE, we can use the concept of proportionality to find the length of AE. Using the given lengths, we can set up the following proportion: AD / AB = CE / AE.

Substituting the values, we have 13 / 10 = 16 / AE. Cross multiplying, we get AE = 10 * 16 / 13 = 160 / 13 = 12.31 (approx.).

Answer 2

`\displaystyle \overline{AE} = 33.8`

Step-by-step explanation:

By triangle similarity theorem we acquire:

`\displaystyle (10)/(16 + 10) = (13)/( AE )`

since AE=AD+ED substitute:

`\displaystyle (10)/(16 + 10) = (13)/( 13 + ED)`

simplify addition:

`\displaystyle (10)/(26) = (13)/( 13 + ED)`

cross multiplication:

`\displaystyle 10(13 + ED) = 26 * 13`

distribute:

`\displaystyle 13 0+ 10ED = 26 * 13`

simplify multiplication:

`\displaystyle 13 0+ 10ED =338`

cancel 130 from both sides:

`\displaystyle10ED =208`

divide both sides by 10:

`\displaystyle \: ED =20.8`

so, the measure of side AE=20.8+13=33.8