The value of x is 9.
Solution:
Proportionality theorem:
If a line is parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
In the given triangle, the middle line is parallel to the base, so the sides are in the same ratio.
Do cross multiplication.
⇒ 9 × 56 = 72(3x – 20)
⇒ 504 = 216 x – 1440
Add 1440 on both sides of the equation.
⇒ 1944 = 216 x
Divide by 216 on both sides of the equation.
⇒ 9 = x
Switch the sides.
⇒ x = 9
The value of x is 9.