Answer:
The value of x is 8 ⇒ B
Step-by-step explanation:
Similar triangles have a constant ratio between their corresponding sides
∵ Δ BCD ~ Δ EFG
∵ The corresponding sides are
- BC and EF
- CD and FG
- DB and GE
- The corresponding sides have a constant ratio
∴ [tex]\frac{BC}{EF}=\frac{CD}{FG}=\frac{DB}{GE}[/tex]
In ΔBCD
∵ ∠C is a right angle
∵ BC = 3 units and DB = 5 units
You can find CD by using Pythagoras Theorem (the sum of the squares of the legs of the right angles is equal to the square of the hypotenuse, the side opposite to the right angle)
∵ BC and CD are the legs of the right angle
∵ DB is the hypotenuse
∵ (DB)² = (BC)² + (CD)²
∴ (5)² = (3)² + (CD)²
∴ 25 = 9 + (CD)²
- Subtract 9 from both sides
∴ 16 = (CD)²
- Take √ for both sides
∴ 4 = CD
∴ CD = 4 units
Let us use the ratio of similarity to find x
∵ BC = 3 units and EF = 6 units
∵ CD = 4 units and FG = x
∵ [tex]\frac{BC}{EF}=\frac{CD}{FG}[/tex]
∴ [tex]\frac{3}{6}=\frac{4}{x}[/tex]
- By using cross multiplication
∴ 3 × x = 6 × 4
∴ 3 x = 24
- Divide both sides by 3
∴ x = 8
The value of x is 8
