Question

Anyone able to help out ?

Answer 1

The value of x is 1

Explanation:

Let us solve the question

∵ Δ PQR ≈ Δ FGH

→ From similarity, then their corresponding sides have an equal ratio

∴
`(PQ)/(FG)` =
`(QR)/(GH)` =
`(PR)/(FH)`

∵ PQ = 3, QR = x + 3, PR = 2

∵ FG = 6, GH = 6x + 2, FH = 4

→ Substitute them in the ratios above

∴
`(3)/(6)` =
`(x+3)/(6x+2)` =
`(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