In Fig. 6.15, if ∆ ABC ~ ∆ DEF and their sides are of lengths (in cm) as marked along them, then find the lengths of the sides of each triangle
Solution:
Given, the triangles ABC and DEF are similar.
The length of the sides are marked in the given figure.
We have to find the length of the sides of each triangle.
Similar triangles have congruent corresponding angles and the corresponding sides are in proportion.
Similar triangles have the same shape, but not the same size.
From the figure,
AB = 2x - 1
BC = 2x + 2
AC = 3x
DF = 6x
EF = 3x + 9
DE = 18
By the property of similarity,
The corresponding sides are in proportion.
So, AB/DE = BC/EF = AC/DF
Now, 2x - 1/18 = 2x + 2/3x + 9 = 3x/6x
Taking 2x - 1/18 = 3x/6x
2x - 1/18 = 1/2
2(2x - 1) = 18
4x - 2 = 18
4x = 18 + 2
4x = 20
x = 20/4
x = 5
Substitute the value of x to find the length of sides of the triangle.
Now, AB = 2(5) - 1 = 10 - 1 = 9
BC = 2(5) + 2 = 10 + 2 = 12
AC = 3x = 3(5) = 15
DF = 6(5) = 30
EF = 3(5) + 9 = 15 + 9 = 24
Therefore, the length of the sides of the triangle are AB = 9 cm, BC = 12 cm, AC = 15 cm, DE = 18 cm, EF = 24 cm and DF = 30 cm.
✦ Try This: Let ABC and DEF be two triangles in which AB = DE, BC = FD and CA = EF. The two triangles are congruent under the correspondence ABC ↔________
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 6
NCERT Exemplar Class 10 Maths Exercise 6.4 Sample Problem 4
In Fig. 6.15, if ∆ ABC ~ ∆ DEF and their sides are of lengths (in cm) as marked along them, then find the lengths of the sides of each triangle
Summary:
In Fig. 6.15, if ∆ ABC ~ ∆ DEF and their sides are of lengths (in cm) as marked along them, then the lengths of the sides of each triangle are AB = 9 cm, BC = 12 cm, AC = 15 cm, DE = 18 cm, EF = 24 cm and DF = 30 cm
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