Answer:
value of sides YZ is 36 cm
Step-by-step explanation:
Similar triangles states that the length of the corresponding sides are in proportion.
Given that: ΔABC is similar to ΔXYZ
then;
Corresponding sides are in proportion i.e
.....[1]
As per the statement:
side AB = 6 cm, side BC =18 cm and side XY = 12 cm.
Substitute these in [1] to solve for side YZ;

or

By cross multiply we have;
cm
Therefore, the value of sides YZ is 36 cm
In centre is the centre of a circle that is inscribed in a triangle, called the incircle, i.e. circle is tangent to all three sides AND located inside the triangle. An incircle is roughly sketched in the accompanying diagram.
Since all radii of an incircle are equal, we have
4x-1=6x-5
Solving for x,
6x-4x=5-1
x=2
consequently, distance from incentre to each side of the triangle is
4(2)-1=7
check 6x-5=6(2)-5=7... checks.
Answers:
The value of x = 2
The distance from incentre to side of triangle is 7