Question

What type of triangle is defined by the following set of side lengths

10, 9, 5



Acute


Obtuse


Right


Not a triangle

Answer 1

Hello there.

Question:

What type of triangle is defined by the following set of side lengths

10, 9, 5

Answer:

Acute

Explanation:

The triangle perimeter is the sum of the lengths of its three sides.

`p=a+b+c=10+9+5=24`

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.

`s=(p)/(2) =(24)/(2) =12`

using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known.

`T=√(s(s-a)(s-b)(s-c))`

`T=√(12(12-10)(12-9)(12-5))`

`T=√(504)=22.45`

There you go :) I even calculated it for you.

Hope this helps!

If you have any questions please ask.

Answer 2

Acute

Explanation:

Hope it helps you in your learning process.