Jika luas sebuah persegi adalah 144 cm², maka keliling bangun tersebut adalah….
Answer (4)
L oo k a t t h e p i c t u re . ∣ B D ∣ = a 2 ∣ B D 1 ∣ = ∣ D B 1 ∣ = a 3 ∣ BE ∣ = ∣ D E ∣ = 2 a 3 U se l a w o f cos in e : ( a 2 ) 2 = ( 2 a 3 ) 2 + ( 2 a 3 ) 2 − 2 ⋅ 2 a 3 ⋅ 2 a 3 ⋅ cos θ 2 a 2 = 4 3 a 2 + 4 3 a 2 − 2 3 a 2 cos θ
2 3 a 2 cos θ = 4 6 a 2 − 2 a 2 2 3 a 2 cos θ = 4 6 a 2 − 4 8 a 2 2 3 a 2 cos θ = − 4 2 a 2 2 3 a 2 cos θ = − 2 a 2 / ⋅ 3 a 2 2 cos θ = − 3 1
Vector for one diagnol (1,1,1) - (0,0,0) = (1,1,1) Vector for another diagnol (0,1,1) - (1,0,0) = (-1,1,1)
Do cos product of two vectors , that is
sqrt(3) sqrt(3) cos(theta) = (1,1,1).(-1,1,1) 3cos(theta) = 1.(-1) + 1.(1) + 1.(1) = 1
therefore cos(theta) = 1/3 angle betwwen diagnols = cos-1 (1/3)
The angle between any two diagonals of a cube is cos − 1 ( 3 1 ) . This is demonstrated using vector calculations of the diagonals and applying the law of cosines. By considering different diagonal pairs, we arrive at the same conclusion consistently.
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Jawaban:48 cmPenjelasan dengan langkah-langkah:Panjang sisi= √Luas= √144= 12 cmKeliling= 4 × s= 4 × 12 cm= 48 cm[tex]\boxed{ \red{ \boxed{\pink{\mathcal{M \frak{ ilana} \purple{ \tt01}}}}}} [/tex]
