Answer: The value of x is 7 cm.
Step-by-step explanation:
Let ABC is a triangle with mid -segment DE parallel to the base BC.
the left side is labeled 40 cm below the mid -segment
i.e. BD = 40 cm
the left side is labeled 5 cm above the mid -segment
i.e. AD = 5 cm
Similarly,
The right side is labeled 2 x + 10 cm below the mid -segment
i.e. EC = 2x+10
The right side is labeled 3 cm above the mid -segment
i.e. AE = 3 cm
So, By Basic proportionality theorem,
The ratio of the other two sides is equal.
[tex]\frac{AD}{DB}=\frac{AE}{EC}\\\\\frac{5}{40}=\frac{3}{2x+10}\\\\\frac{1}{8}=\frac{3}{2x+10}\\\\2x+10=24\\\\2x=24-10\\\\2x=14\\\\x=\frac{14}{2}\\\\x=7 cm[/tex]
Hence, the value of x is 7 cm.
