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)

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