Jawab:

C. 7√2 / 2 cm

Penjelasan dengan langkah-langkah:

Diketahui:
Luas sisi-sisi balok berturut turut

9 cm², 6 cm², dan 3 cm²

Ditanya:

Panjang diagonal ruang balok

Jawab:

Luas sisi balok

9 cm², 6 cm², dan 3 cm²

Misalkan

p × l = 9 cm²

p × t = 6 cm²

l × t = 3 cm²

pl × pt × lt = 9 cm² × 6 cm² × 3 cm²

(p × p) × (l × l) × (t × t) = 162 cm⁶

p² × l² × t² = 162 cm⁶

(p × l × t)² = 162 cm⁶

p × l × t = √(162 cm⁶)

p × l × t = √((81 × 2) cm⁶)

p × l × t = 9√2 cm³

• (p × l = 9 cm²)

9 cm² × t =  9√2 cm³

t = 9√2 cm³

t = 9√2 cm³ / 9 cm²

t = √2 cm

• (p × t = 6 cm²)

p × √2 cm = 6 cm²

p = 6 cm² / (√2 cm)

p = 6√2 / 2 cm = 3√2 cm

• (l × t = 3 cm²)

l × √2 cm = 3 cm²

l = 3 cm² / (√2 cm)

l = 3√2 / 2 cm

Panjang diagoal ruang balok

= √(p² + l² + t²)

= √((3√2 cm)² + (3√2 / 2 cm)² + (√2 cm)²)

= √ ((18 cm²) + (9/2 cm²) + (2 cm²))

= √ (20 cm² + 9/2 cm²)

= √((40 + 9)/2) cm²)

=√49/2 cm²

= 7/√2 cm

= 7√2/2 cm (C)