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3 years ago

PLZ HELP ASAP SIMILARITY

Mathematics

1 answer:

PIT_PIT [208]3 years ago

7 0

LY = 5.2 , TY = 3.9
Δ LTN is a right triangle , ∠T = 90° , TY⊥LN
∴ TY² = LY * YN
∴ 3.9² = 5.2 * YN
∴ YN = 3.9²/5.2 = 2.925

∴ LN = LY + YN = 5.2 + 2.925 = 8.125

Δ LYT is a right triangle , ∠Y = 90°
LT² = LY² + YT² = 5.2² + 3.9² = 42.25
∴ LT = √42.25 = 6.5

Δ NYT is a right triangle , ∠Y = 90°
NT² = NY² + YT² = 2.925² + 3.9² = 23.765
∴ NT = √23.765 = 4.875

The preimeter of the rectangle LINT = 2 * (LT + TN)
                                                          = 2 * ( 6.5 + 4.875 )
                                                          = 2 * 11.375
                                                          = 22.75

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