#1**-1 **

By Heron's formula, the area of the triangle is 90. So the shortest altitude, which is opposite the longest side, is 2*90/26 = 90/13.

Guest Jul 14, 2020

#6**+5 **

Heron's formula is \(\sqrt{s(s-a)(s-b)(s-c)}=area\) where s is the semi-perimeter (in less fancy words \(\frac{area}{2}\)) and a, b, c are the sides of the triangle. I'm pretty sure the guest did something wrong in the calculations there and that is why he/she was wrong

amazingxin777
Jul 14, 2020

#3**0 **

Right scalene triangle.

Sides: a = 10 b = 24 c = 26

**Area: T = 120**

Perimeter: p = 60

Semiperimeter: s = 30

Angle ∠ A = α = 22.62° = 22°37'11″ = 0.395 rad

Angle ∠ B = β = 67.38° = 67°22'49″ = 1.176 rad

Angle ∠ C = γ = 90° = 1.571 rad

Height: ha = 24

Height: hb = 10

**Height: hc = 9.231 ==[2 x 120] / 26 ==9.231 - The shortest altitude.**

Guest Jul 14, 2020