What is the area of a triangle whose sides measure 13 inches, 15 inches, and 24 inches?

Enter your answer, in simplified radical form, in the box.

_____ inches squared

jjennylove Apr 17, 2020

#1**+2 **

We can use a theorem in geometry known as "heron's formula". It states that given semi-perimeter(half of the perimeter) of triangle ABC as *s*, we have:

[ABC] = \(\sqrt{s(s-a)(s-b)(s-c)}\)

The semi perimeter of this triangle is:

\({13+15+24\over2} = {52\over2} = 26\)

We then have:

[ABC] = \(\sqrt{26(26-13)(26-15)(26-24)} = \sqrt{26*13*11*2} = \sqrt{26*26*11}\)

we can then take out a 26 from the square term, which gets us:

\(26\sqrt{11}\) in^{2} as our area

jfan17 Apr 17, 2020

#3**+1 **

i remember this now! it makes sense thank you for your explaination . it really helped!

jjennylove
Apr 17, 2020