The height of a triangle is 5 m less than half its base. If the area of the triangle is 300 m2, how do you find the measure of the height?

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Answer 1 · 2016-08-18T18:58:27

height#=15" meters"#

The formula for area of the triangle is #A = (bh)/2#.

Let the base be #b# and the height be #b/2 - 5#.

Then:

#300 = (b(b/2 - 5))/2#

#600 = b(b/2 - 5)#

#600 = b^2/2 - 5b#

#600 = (b^2 - 10b)/2#

#1200 = b^2 - 10b#

#b^2 - 10b - 1200= 0#

#1(b^2 - 10b + 25 -25) = 1200#

#1(b^2 - 10b + 25) - 25 = 1200#

#(b - 5)^2 = 1225#

#b - 5 = +-35#

#b = -30 and 40#

Hence, the base measures #40" meters" (a negative length is impossible).

The height therefore measures #40/2 - 5 = color(green)(15)#

Hopefully this helps!