Question 76799
Since the problem is about a right triangle, think about using the Pythagorean theorem: {{{c^2 = a^2 + b^2}}} Where: c is the length of the hypotenuse and a & b are the lengths of the two legs.
In this problem, you are given the length of one of the legs (11 m.) and you are told that the length of the hypotenuse is 1 meter longer than the other (longer) leg.
So, we'll let x meters be the length of the longer leg.
Then the length of the hypotenuse will be x+1 meters.
Now let's apply the Pythagorean theorem.
{{{(x+1)^2 = 11^2 + x^2}}} Simplify this.
{{{x^2+2x+1 = 121 + x^2}}} Subtract {{{x^2}}} from both sides of the equation.
{{{2x+1 = 121}}} Now subtract 1 from both sides.
{{{2x = 120}}} Finally, divide both sides by 2.
{{{x = 60}}}
The length of the longer leg is 60 meters.