Question

find the area of the triangle whose sides are 5 ft, 12 ft, and 13 ft. find the height of the triangle corresponding to the longest side.

Answer 1

according to heron's formula area of triangle =
$\sqrt{s(s - a)( s-b)(s -c ) }$
perimeter of triangle = 5+12+13=30ft
s=30/2= 15
therefore area =
$\sqrt{15(15 - 5)(15 - 12)(15 - 13)}$
$\sqrt{15 \times 10 \times 3 \times 2}$
$2 \times 3 \times 5$
${30ft}^{2}$
height of the triangle corresponding to the largest side = 2(area)/side
=2(30)/13
=60/13
=4.61
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hope it helps