The hypotenuse of an isosceles right triangle is one meter longer than either of its legs. Find the length of each side

Question

Need help with this math problem in my homework packet

Answer 1

Draw the isos. rt. triangle; label its legs x (each) and label hypotenuse (x+1)

 

Now use the Pythagorean Theorem.  Easy!  Remember, the square of the hypotenuse will be a TRINOMIAL x² + 2x + 1.

Answer 2

The legs are the same length since this is isosceles.

Call that length x

The hypotenuse is 1 meter longer ...  x+1

 

x²+x² = (x+1)²    from Pythagorean Theorem

 

2x² = x² + 2x + 1

 

x² - 2x - 1 = 0

 

From quadratic formula:  x = [-b±√(b²-4ac)]/2a

 

x = [2 ±√((-2)²-4(1)(-1))]/[(2)(1)]

 

x = [2 ±√8]/2

 

Finishing this out and discarding the negative answer

will give you the length of the legs.

The hypotenuse will then be x+1

 

Answer 3

a = x

b = x

c = x+1

 

Pythagorean Theorem

 

a^2+b^2=c^2

 

x^2 + x^2 = (x+1)^2

 

2x^2 = x^2+2x+1

 

x^2-2x-1 = 0

 

Now use the quadratic equation

 

where a = 1, b = -2 , c = -1

 

x=1+sqrt(2)

 

each base is 1 + sqrt(2)

 

the hypotenuse is 2 + sqrt(2)