LOSMIMath - Can you calculate area of the triangle? | (Perimeter) |

[@bikerrick]

I would really like to see one of our you tube math teachers give real numbers that I could measure, it would help to understand what your answers mean.

[@MrPaulc222]

Call the short side a. As it's a 30,60,90, 3a + a*sqrt(3) = 48. a*sqrt(3) = 48 - 3a Square both sides: 3a^2 = 2304 - 288a + 9a^2. 6a^2 - 288a + 2304 = 0 All are divisible by 6: a^2 - 48a + 384 = 0 (48+or-sqrt(2304 - 4*384))/2 = a (48+or-sqrt(768))/2 = a (48+or-2*sqrt(192))/2 = a (48+or-4*sqrt(48))/2 = a (48+or-8*sqrt(12)/2 = a (48+or-16*sqrt(3))/2 = a a = 24+or-8*sqrt(3) The "+" solution would have the shortest side as about 38, so discard that, so a = 24-8*sqrt(3) (24 - 8*sqrt(3) * (24*sqrt(3) - 24) Approx (24 - 13.86) * (17.57) 10.14 * 17.57 As one of them must be halved, 5.07 * 17.57 89.076 (rounded). I see I'm a little out, but that's probably because I rounded to decimal a bit earlier than usual.