D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE||BC. Then, length of DE (in cm) is
a. 2.5
b. 3
c. 5
d. 6
Solution:
Given, D and E are the points on the sides AB and AC of a triangle ABC.
The length of the segment
AD = 2 cm
BD = 3 cm
BC = 7.5 cm
Also, DE||BC
We have to find the length of DE.
Consider the triangles △ADE and △ABC.
Since DE || BC, the corresponding angles are equal.
∠ADE = ∠ABC
∠AED= ∠ACB
Thus by AA similarity we find △ADE and △ABC are similar.
△ADE ~ △ABC
If two triangles are similar, then their sides are proportional.
AE/AC = DE/BC = AD/AB
So, AD/AB = DE/BC
AB = AD + BD = 2 + 3 = 5 cm
2/5 = DE/7.5
On cross multiplication,
2(7.5) = (5)DE
DE = 15/5
DE = 3 cm
Therefore, the length of DE is 3cm.
✦ Try This: D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 1 cm, BD = 2 cm, BC = 4 cm and DE||BC. Then, length of DE (in cm) is -----------
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.1 Sample Problem 2
D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE||BC. Then, length of DE (in cm) is, a. 2.5, b. 3, c. 5, d. 6
Summary:
D and E are respectively the points on the sides AB and AC of a triangle ABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE||BC. Then, the length of DE (in cm) is 3 cm.
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