In Fig. 6.12, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD
Solution:
Given, ∠ACB = ∠CDA
Also, AC = 8 cm
AD = 3 cm
We have find BD.
In △ADC and △ACB,
Given, ∠ACB = ∠CDA
∠CAD = ∠BAC = common angle
AAA criterion states that if two angles of a triangle are respectively equal to two angles of another triangle, then by the angle sum property of a triangle their third angle will also be equal.
By AAA criterion, the third angle will be equal.
Therefore, the triangles ADC and ACB are similar.
By the property of similar triangles,
The corresponding sides are proportional.
So, AC/AD = AB/AC
8/3 = AB/8
On cross multiplication,
8(8) = 3AB
AB = 64/3
Now, BD = AB - AD
= 64/3 - 3
= (64 - 9)/3
= 55/3
BD = 18.33 cm
Therefore, the length of BD is 18.33 cm
✦ Try This: In the figure, if ∠ACB = ∠CDA,AC = 6 cm and AD = 3 cm, then find the length of AB.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 13
In Fig. 6.12, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, find BD
Summary:
In Fig. 6.12, if ∠ACB = ∠CDA, AC = 8 cm and AD = 3 cm, then BD = 18.33 cm
☛ Related Questions:
- A 15 metres high tower casts a shadow 24 metres long at a certain time and at the same time, a telep . . . .
- Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Fi . . . .
- Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller t . . . .