Question

The hypotenuse of a right triangle is 13.0, and one leg is 9.0 units shorter than the other. Find the dimensions of the figure (rounded to the nearest tenth)

Answer 1

Let, one leg be x units. 
since the other leg is 9.0 units shorter than the other, 
the measure of the other leg =x-9 
hypotenuse =13.0 units 
According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.  
x^2 +(x-9)^2 =13^2 
x^2 + x^2 -18x +81 = 169 
2x^2-18x-88=0 
Divide the whole equation by 2 
x^2 - 9x -44 =0  
Let's use the quadratic formula to find the roots. 
formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a  
a=1 b=-9 c=-44 
x= [9±sqrt(81+176)]/2
 =[9±sqrt(257)]/2
 =[9±16.03]/2
 =25.03/2 or -7.03/2
 length of a triangle cannot be negative,
 Therefore, x=25.03/2 =12.52 
 one leg =12.5 units
 other leg =12.52-9 =3.5 units