Question

If angle ACB is equal to angle CDA, AC=6cm and AD=3cm, then find the length of AB.

Answer 1

Answer: The length of AB is 12 cm.

Step-by-step explanation:

Given data:

∠ACB = ∠CDA

AC = 6 cm

AD = 3 cm

To find: Length of AB

From the figure attached below, in ∆ ABC & ∆ ACD, we have

∠A = ∠A ….. [∵ common angle for both the triangle]

∠ACB = ∠CDA ….. [∵ given]

∴ By AA similarity, ∆ABC ~ ∆ACD

Since the sides of two similar triangles are proportional to each other

∴ $\frac{AB}{AC}$ = $\frac{AC}{AD}$ = $\frac{BC}{CD}$

Now taking,

$\frac{AB}{AC}$ = $\frac{AC}{AD}$

⇒ AC² = AB * AD

⇒ 6² = AB * 3 …… [given AC = 6 cm & AD = 3 cm]

⇒ 36 = AB * 3

⇒ AB = 36/3 = 12 cm

Answer 2

Secondary School Math 5+3 pts

If angle ACB is equal to angle CDA, AC=6cm and AD=3cm, then find the length of AB.

Ask for details Follow Report by Mahikarunjhun2000 22.09.2019

Answers

Khushimarkam99Ambitious

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BhagyashreechowdhuryAce

Answer: The length of AB is 12 cm.

Step-by-step explanation:

Given data:

∠ACB = ∠CDA

AC = 6 cm

AD = 3 cm

To find: Length of AB

From the figure attached below, in ∆ ABC & ∆ ACD, we have

∠A = ∠A ….. [∵ common angle for both the triangle]

∠ACB = ∠CDA ….. [∵ given]

∴ By AA similarity, ∆ABC ~ ∆ACD

Since the sides of two similar triangles are proportional to each other

∴ AB/AC=AC/AD=BC/CD

Now taking

AB/AC=AC/AD

⇒ AC² = AB * AD

⇒ 6² = AB * 3 …… [given AC = 6 cm & AD = 3 cm]

⇒ 36 = AB * 3

⇒ AB = 36/3 = 12 cm