Answer:
x = 2
Step-by-step explanation:
In the given figure
∵ ABC is a triangle
∵ D is a point on side AB
∵ E is a point on side BC
∵ DE // AC
∵ AC is the third side of the triangle
→ That means DE divides the sides AB, BC into parts that have the same ratio
∴ [tex]\frac{BD}{DA}[/tex] = [tex]\frac{BE}{EC}[/tex]
∵ BD = 6 and DA = 4
∵ BE = x + 1 and EC = x
→ Substitute them in the ratio above
∴ [tex]\frac{6}{4}[/tex] = [tex]\frac{x+1}{x}[/tex]
→ By using the cross multiplication
∵ 6 × x = 4 × (x + 1)
∴ 6x = 4(x + 1)
∴ 6x = 4(x) + 4(1)
∴ 6x = 4x + 4
→ Subtract 4x from both sides
∵ 6x - 4x = 4x - 4x + 4
∴ 2x = 4
→ Divide both sides by 2 to find x
∴ x = 2
