In triangle abc segment de is parallel to the side ac . (the endpoints of segment de lie on the sides ab and bc respectively). what is the length of ad if ab=16cm, ac=20cm, and de=15cm;

The measure of AD from the given diagram is 4 cm

Find the image of the diagram attached below;

Using the similarity theorem of a triangle;

AB/AC = BD/DE

Given the following parameters;

AB=16cm

AC=20cm

DE=15cm

Substituting into the formula will give;

16/20 = BD/15

20BD = 16 * 15

20BD = 240

BD = 12 cm

From the figure, the sum of AD and DB is AB that is:

AD + DB = AB

AD = AB - DB

AD = 16 - 12

AD = 4cm

Hence the measure of AD from the given diagram is 4 cm

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The length of AD is 4 cm

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

- Point D lies on side AB ans point E lies on side BC

- Segment DE parallel to the side AC

- AB = 16 cm , AC = 20 cm , DE = 15 cm

* Lets solve the problem

- In Δ ABC

∵ DE // AC

∴ m∠BDE = m∠BAC ⇒ corresponding angles

∴ m∠BED = m∠BCA ⇒ corresponding angles

* Lets use similarity to prove that Δ BDE similar to Δ BAC

- In triangles BDE and BAC

∵ m∠BDE = m∠BAC

∵ m∠BED = m∠BCA

∵ ∠B is a common angle in the two triangles

∴ Δ BDE ≈ Δ BAC ⇒ by AAA

∴ Their corresponding sides are proportion

∴

∵ AB = 16 cm , AC = 20 cm , DE = 15 cm

∴

∴

- By using cross multiplication

∴ 4 BD = 16 × 3

∴ 4 BD = 48

- Divide both sides by 4

∴ BD = 12 cm

∵ Point D divides side AB into two parts BD and DA

∴ AB = BD + AD

∵ AB = 16 cm

∵ BD = 12 cm

∴ 16 = 12 + AD

- Subtract 12 from both sides

∴ AD = 4 cm

* The length of AD is 4 cm

answer: c

because if you look at the chart you can see a pattern and compare it to the question he simplify out your

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