(a) Write an equation in terms of that represents the given relationship. The equation is

Question

The longer leg of a right triangle is 1

 cm

 longer than the length of the shorter leg x

. The hypotenuse is 29

 cm

(a) Write an equation in terms of 

x

that represents the given relationship.The equation is

Answer 1

29^2 = x^2 + (x+1)^2

29^2= x^2 + x^2 +2x +1

841 = 1+ 2x^2 +2x

2x^2 +2x - 840=0

x^2 +x -420 = 0

x^2 + x + (1/2)^2 = 420 + 1/4

(x+ 1/2)^2 = 420.25

x + 1/2 = sqr420.25

x = -.5 +sqr420.25= -5+ 20.5 = 20

shorter leg = 20 longer leg =21

20^2 + 21^2 = 400 + 441 = 841 = the hypotenuse squared = 29^2