Hello there.
Question:
What type of triangle is defined by the following set of side lengths
10, 9, 5
Answer:
Acute
Step-by-step explanation:
The triangle perimeter is the sum of the lengths of its three sides.
[tex]p=a+b+c=10+9+5=24[/tex]
The semiperimeter of the triangle is half its perimeter. The semiperimeter appears in formulas for triangles to be given a separate name. the triangle inequality, the longest side length of a triangle is less than the semi perimeter.
[tex]s=\frac{p}{2} =\frac{24}{2} =12[/tex]
using Heron's formula
Heron's formula gives the area of a triangle when the length of all three sides is known.
[tex]T=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]T=\sqrt{12(12-10)(12-9)(12-5)}[/tex]
[tex]T=\sqrt{504}=22.45[/tex]
There you go :) I even calculated it for you.
Hope this helps!
If you have any questions please ask.
