Question

In triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). Find DE, if AC=20cm, AB=17cm, and BD=11.9cm;

Answer 1

To find the length of DE in triangle ABC, with DE parallel to AC, we use similar triangles. AD and DE are in proportion to AB and AC, respectively. After calculating, we find that DE is approximately 6cm.

Step-by-step explanation:

To find the length of segment DE in triangle ABC, where DE is parallel to side AC, we can apply the concept of similar triangles. Since DE is parallel to AC, triangles ADE and ABC are similar by the AA (Angle-Angle) criterion. This means that the corresponding sides of the triangles are in proportion.

Given that AC = 20cm and AB = 17cm, and BD = 11.9cm, we first need to find the length of AD (which we'll call x) and then can find DE. Because triangles ADE and ABC are similar:

1. AD/AB = DE/AC
2. x/17 = DE/20

But, since AB = AD + DB, we get:

1. 17 = x + 11.9
2. x = 17 - 11.9
3. x = 5.1cm

Now we can solve for DE:

1. 5.1/17 = DE/20
2. DE = 20 * (5.1/17)
3. DE = 6cm (after rounding)

Therefore, the length of segment DE is approximately 6cm.

Answer 2

The length of DE is 14 cm.

Step-by-step explanation:

Given in triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). we have to find the length of DE.

Given lengths are AC=20cm, AB=17cm, and BD=11.9cm

In ΔBDE and ΔBAC

∠BDE=∠BAC (∵Corresponding angles)

∠BED=∠BCA (∵Corresponding angles)

By AA similarity rule, ΔBDE~ΔBAC

∴their corresponding sides are in proportion

⇒
`(BE)/(BC)=(BD)/(BA)=(DE)/(AC)`

⇒
`(BD)/(BA)=(DE)/(AC)`

⇒
`(11.9)/(17)=(DE)/(20)`

⇒
`DE=(20* 11.9)/(17)=14cm`