algebra problem

Question

The shortest side of a right triangle measures 7 m. The lengths of the other two sides are consecutive integers? - the hypotenuse being the longer of the two. Find the lengths of the other two sides.

Answer 1

c = length of hypotenuse

 

a = 7

 

b = x

 

c = x + 1

 

c² = a² + b² = 7² + x² = (x + 1)²

 

49 + x² = x² + 2x + 1

 

49 = 2x + 1

 

x = (49 - 1)/2 = 48/2 = 24

 

The lengths of the other two sides are 24 m and (24+1)=5 m