Construct a triangle similar to $ \triangle A B C $ in which $ A B=4.6 \mathrm{~cm}, \mathrm{BC}=5.1 \mathrm{~cm}, \angle A=60^{\circ} $ with scale factor $ 4: 5 $.

Given:

A \( \triangle A B C \) with sides \( A B=4.6 \mathrm{~cm}, \mathrm{BC}=5.1 \mathrm{~cm}, \angle A=60^{\circ} \).

To do:

We have to construct a triangle similar to \( \triangle A B C \) in which \( A B=4.6 \mathrm{~cm}, \mathrm{BC}=5.1 \mathrm{~cm}, \angle A=60^{\circ} \) with scale factor \( 4: 5 \).

Solution:

Steps of construction:

(i) Draw a line segment $AB = 4.6\ cm$.

(ii) At $A$, draw a ray $AX$ making an angle of $60^o$.

(iii) With centre $B$ and radius $5.1\ cm$ draw an arc intersecting $AX$ at $C$.

(iv) Join $BC$.

$ABC$ is the required triangle.

(v) From $A$, draw a ray $AX$ making an acute angle with $AB$ and cut off five equal parts making $AA_1 = A_1A_2 = A_2A_3 = A_3A_4=A_4A_5$.

(vi) Join $A_4$ and $B$.

(vii) From $A_5$, draw $A_5B’$ parallel to $A_4B$ and $B’C’$ parallel to $BC$.

$C’AB’$ is the required triangle.

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Updated on: 10-Oct-2022

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