Question 112425
Since the question asks for the length of the longer leg, let's use x to denote this length.


We are told that the hypotenuse of the triangle is 40 meters longer than the longer leg, so the hypotenuse must be x + 40.


Pythagoras tells us that in any right triangle with legs a and b and hypotenuse c, the following is true:


{{{c^2=a^2+b^2}}}.


In our problem, a = 120 meters, b = x meters, and c = x + 40 meters.  Therefore:


{{{(x+40)^2=120^2+x^2}}}


{{{x^2+80x+1600=14400+x^2}}}
{{{80x+1600=14400}}}
{{{80x=12800}}}
{{{x=160}}}, so the longer leg is 160 meters.  And, by the way, the hypotenuse must be 200 meters (160 + 40)


Does this answer make sense?


First, x is supposed to be the longer leg, and 160 is larger than 120.  It is also 40 meters smaller than the 200 meter hypotenuse.


Also, 120:160:200 reduces to 3:4:5, and we know that a 3, 4, 5 triangle is a right triangle.


Hope this helps.
John