Question 75949
One leg of a right triangle is 2 inches smaller than the hypotenuse. The other leg is 5 inches long. What are the lengths of the unknown leg and hypotenuse?
The Pythagorean theorem says the hypotenuse squared = leg squared + other leg squared c^2=a^2+b^2
Let the hypotenuse be: x
Then the leg that is two inches smaller than the hypotenuse is: x-2
The other leg is: 5
{{{x^2=(x-2)^2+5^2}}}
{{{x^2=x^2-4x+4+25}}}
{{{x^2=x^2-4x+29}}}
{{{x^2-x^2=x^2-x^2-4x+29}}}
{{{0=-4x+29}}}
{{{0-29=-4x+29-29}}}
{{{-29=-4x}}}
{{{-29/-4=-4x/-4}}}
{{{7.25=x}}}
The hypotenuse is x=7.25 in
The missing leg is x-2=7.25-2=5.25 in
Happy Calculating!!!!