If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ ABC
Solution:
Given, the triangles ABC and DEF are similar.
The length of the sides
AB = 4 cm
DE = 6 cm
EF = 9 cm
FD = 12 cm.
We have to find the perimeter of the triangle ABC.
By the property of similar triangles,
Since, ∆ABC ~ ∆DEF the corresponding sides are proportional.
AB/DE = BC/EF = AC/DF
Taking AB/DE = BC/EF
4/6 = BC/9
On cross multiplication,
9(4) = 6(BC)
BC = 36/6
BC = 6 cm
Taking BC/EF = AC/DF
6/9 = AC/12
On cross multiplication,
12(6) = 9(AC)
AC = 12(6)/9
AC = 8 cm
Therefore, the length of the sides of the triangle ABC are AB = 4 cm, BC = 6 cm and AC = 8 cm.
Perimeter = AB + BC + AC
= 4 + 6 + 8
= 18 cm
Therefore, the perimeter of the triangle ABC is 18 cm.
✦ Try This: If ∆ABC~∆DEF such that 2AB = DE and BC = 6cm, find EF
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.3 Problem 7
If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of ∆ ABC
Summary:
If ∆ABC ~ ∆DEF, AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm,then the perimeter of ∆ ABC is 18 cm
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