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?

Question

3638 views around the world

You can reuse this answer
Creative Commons License

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!