Question

If HL=16, LI =9, and HK = 24, find KJ to the nearest hundredth.

Answer 1

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According to the figure ;

LK || IJ

If there are two parallel sides in a triangle, we can use the Thales theorem.

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According to the Thales theorem we have :

`(HL)/( LI ) = (HK)/(KJ) \\`

Thus :

`(16)/(9) = (24)/( KJ) \\`

Multiply sides by KJ

`KJ * (16)/(9) = 24 \\`

Multiply sides by 9

`KJ * 16 = 24 * 9`

Divided sides by 16

`KJ = (24 * 9)/(16) \\`

`KJ = (8 * 3 * 9)/(8* 2) \\`

8 s simplifies

`KJ = (3 * 9)/(2) \\`

`KJ = (27)/(2) \\`

`KJ = (26 + 1)/(2) \\`

`KJ = (26)/(2) + (1)/(2) \\`

`KJ = 13 + 0.50`

`KJ = 13.50`

Done....

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