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!