Diketahui 1 balok dengan perbandingan P : L : T = 4 : 2 : 3.Jika luas permukaan balok 800 cm ².Hitunglah = A.Panjang diagonal alas B.Panjang diagonal sisi kanan

[tex]800 = 2(4x \times 2x) + 2(4x \times 3x) + 2(2x \times 3x) \\ 800 = 16 {x}^{2} + 24 {x}^{2} + 12 {x}^{2} \\ 800 = 52 {x}^{2} \\ x = \sqrt{ \frac{200}{13} } \\ x = 10 \sqrt{ \frac{2}{13} } [/tex]
p= 40√²/13
l =20√²/13
t = 30√²/13
diagonal alas
[tex] = \sqrt{ {(40 \sqrt{ \frac{2}{13} } })^{2} + ( {20 \sqrt{ \frac{2}{13} }) }^{2}} \\ = \sqrt{ \frac{3200}{13} + \frac{800}{13} } \\ = 20 \sqrt{ \frac{10}{13} } [/tex]
diagonal sisi samping
[tex] = \sqrt{ ({20 \sqrt{ \frac{2}{13} } })^{2} + ( {30 \sqrt{ \frac{2}{13} } })^{2} } \\ = \sqrt{ \frac{800}{13} + \frac{1800}{13} } \\ = \sqrt{ 200 } \\ = 10 \sqrt{2} [/tex]
diagonal ruang
[tex] = \sqrt{( {30 \sqrt{ \frac{2}{13} } })^{2} + ( {20 \sqrt{ \frac{10}{13} } })^{2} } \\ = \sqrt{ \frac{1800}{13} + \frac{4000}{13} } \\ = 10 \sqrt{ \frac{58}{13} } [/tex]