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valina [46]
2 years ago
13

Anyone able to help out ?

Mathematics
1 answer:
LenKa [72]2 years ago
4 0

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

∴ \frac{PQ}{FG} = \frac{QR}{GH} = \frac{PR}{FH}

∵ PQ = 3, QR = x + 3, PR = 2

∵ FG = 6, GH = 6x + 2, FH = 4

→ Substitute them in the ratios above

∴ \frac{3}{6} = \frac{x+3}{6x+2} = \frac{2}{4}

→ 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

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