Question

Help please!

Answer 1

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

∴ $\frac{BD}{DA}$ = $\frac{BE}{EC}$

∵ BD = 6 and DA = 4

∵ BE = x + 1 and EC = x

→ Substitute them in the ratio above

∴ $\frac{6}{4}$ = $\frac{x+1}{x}$

→ 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