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.
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.
Assume a 3, 4, 5 triangle. Multiply each side by 4. Thus, we have short side = 12, Height = 16, and Hypotenuse = 20. Now, add all three sides and you get 12 + 16 + 20 = 48. That's indeed our perimeter length. Now use area for a triangle formula of 1/2 base times height to get 1/2(12) * 16 = 96. Therefore, the CORRECT answer to your problem is 96!!! Simple! 😏
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.
You should have simplified to 384*sqrt(3)-576.
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.
(1 + 2 + √3)x = 48
x = 48/(3 + √3) = 48(3 - √3)/6 = 8(3 - √3)
area = (√3)(1/2)(64)(3 - √3)^2 = 32(√3)(12 - 6√3) = 192(√3)(2 - √3) = 192(2√3 - 3) = 384√3 - 576
Area ≈ 89.11
Assume a 3, 4, 5 triangle. Multiply each side by 4. Thus, we have short side = 12, Height = 16, and Hypotenuse = 20. Now, add all three sides and you get 12 + 16 + 20 = 48. That's indeed our perimeter length. Now use area for a triangle formula of 1/2 base times height to get 1/2(12) * 16 = 96. Therefore, the CORRECT answer to your problem is 96!!! Simple! 😏
30° - 60° - 90° corresponds to a 1 - √3 - 2 triangle
about 89
Please spell check.
yes i noticed perimeter and hypotenuse ?