FIND MISSING LENGTH OF SIMILAR TRIANGLES

Find the missing length. The triangles in each pair are similar.

Problem 1 :

findmislentriq1

Solution:

Because the above triangle ∆ PQR and ∆ EDC are similar, the ratios of the corresponding sides will be equal.

RQCD=PQED30x=256525×x=30×6525x=1950x=195025x=78

Problem 2 :

findmislentriq2

Solution:

Because the above triangle ∆ DCE and ∆ KJL are similar, the ratios of the corresponding sides will be equal.

Let x = DC

DCKJ=DEKLx65=634545×x=63×6545x=4095x=409545x=91

Problem 3 :

findmislentriq3

Solution:

Because the above triangle ∆ ABC and ∆ AKL are similar, the ratios of the corresponding sides will be equal.

AKAC=KLCB=ALAB936=1248=13x1248=13x12×x=13×4812x=624x=62412x=52

Problem 4 :

findmislentriq4

Solution:

Because the above triangle ∆ HJG and ∆ KJL are similar, the ratios of the corresponding sides will be equal.

HJKJ=GJLJ4066=30x40×x=30×6640x=1980x=198040x=49.5

Solve for x. The triangles in each pair are similar.

Problem 5 :

findmislentriq5

Solution:

Because the above triangle ∆ RQP and ∆ FGH are similar, the ratios of the corresponding sides will be equal.

PQGH=RQFG1232=214x+1612×(4x+16)=32×2148x+192=67248x = 672-19248x=480x=48048x=10

Problem 6 :

findmislentriq6

Solution:

Because the above triangle ∆ EDT and ∆ VTU are similar, the ratios of the corresponding sides will be equal.

ETVU=DTTU4815x+12=5615448×154=56×(15x+12)7392=840x+672840x=7392-672840x=6720x=6720840x=8

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