It is given that ∆ ABC ~ ∆ EDF such that AB = 5 cm, AC = 7 cm, DF= 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles
Solution:
Given, ∆ ABC ~ ∆ EDF
The length of the sides
AB = 5 cm
AC = 7 cm
DF = 15 cm
DE = 12 cm
We have to find the length of the remaining sides of the triangles.
Similar triangles have congruent corresponding angles and the corresponding sides are in proportion.
Similar triangles have the same shape, but not the same size.
By the property of similarity,
The corresponding sides are proportional.
So, AB/ED = BC/DF = AC/EF
5/12 = BC/15 = 7/EF
Considering 5/12 = BC/15,
15(5) = 12BC
BC = 15(5)/12
BC = 5(5)/4
BC = 25/4
BC = 6.25 cm
Considering 5/12 = 7/EF
On cross multiplication,
5EF = 12(7)
EF = 12(7)/5
EF = 84/5
EF = 16.8 cm
Therefore, the lengths of the remaining sides BC and EF are 6.25 cm and 16.8 cm.
✦ Try This: It is given that ∆ ABC ~ ∆ EDF such that AB = 6 cm, AC = 8 cm, DF= 13 cm and DE = 10 cm. Find the lengths of the remaining sides of the triangles.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.4 Problem 2
It is given that ∆ ABC ~ ∆ EDF such that AB = 5 cm, AC = 7 cm, DF= 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles
Summary:
It is given that ∆ ABC ~ ∆ EDF such that AB = 5 cm, AC = 7 cm, DF= 15 cm and DE = 12 cm. The lengths of the remaining sides of the triangles BC and EF are 6.25 cm and 16.8 cm
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