The formula for the area of a triangle is:
#A = (h_b b)/2#
Where:
#A# is the area of the triangle.
#h_b# is the height of the triangle from the base
#b# is the length of the base of the triangle.
Substituting the information in the problem and solving for #h_b# gives:
#3.6"in"^2 = (h_b 2.4"in")/2#
#color(red)(2) xx 3.6"in"^2 = color(red)(2) xx (h_b 2.4"in")/2#
#7.2"in"^2 = cancel(color(red)(2)) xx (h_b 2.4"in")/color(red)(cancel(color(black)(2)))#
#7.2"in"^2 = h_b 2.4"in"#
#(7.2"in"^2)/color(red)(2.4"in") = (h_b 2.4"in")/color(red)(2.4"in")#
#(7.2"in"^color(red)(cancel(color(black)(2))))/color(red)(2.4color(black)(cancel(color(red)("in")))) = (h_b color(red)(cancel(color(black)(2.4"in"))))/cancel(color(red)(2.4"in"))#
#(7.2"in")/color(red)(2.4) = h_b#
#3"in" = h_b#
#h_b = 3"in"#
The height of the triangle in the problem is #3# inches
