Answer:
The value of x is 1
Step-by-step explanation:
Let us solve the question
∵ Δ PQR ≈ Δ FGH
→ From similarity, then their corresponding sides have an equal ratio
∴ [tex]\frac{PQ}{FG}[/tex] = [tex]\frac{QR}{GH}[/tex] = [tex]\frac{PR}{FH}[/tex]
∵ PQ = 3, QR = x + 3, PR = 2
∵ FG = 6, GH = 6x + 2, FH = 4
→ Substitute them in the ratios above
∴ [tex]\frac{3}{6}[/tex] = [tex]\frac{x+3}{6x+2}[/tex] = [tex]\frac{2}{4}[/tex]
→ By using cross multiplication between the first two ratios
∵ 3 × (6x + 2) = 6 × (x + 3)
∴ 3(6x + 2) = 6(x + 3)
∴ 3(6x) + 3(2) = 6(x) + 6(3)
∴ 18x + 6 = 6x + 18
→ Subtract 6x from both sides
∵ 18x - 6x + 6 = 6x - 6x + 18
∴ 12x + 6 = 18
→ Subtract 6 from both sides
∵ 12x + 6 - 6 = 18 - 6
∴ 12x = 12
→ Divide both sides by 12
∴ x = 1
