Question

The hypotenuse of a right triangle is 10cm long. The longer leg is 2cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg: __cm
Length of the longer leg: __cm
Length of the hypotenuse: __cm

Answer 1

We need Pythagoras theorem here
a^2+b^2 = c^2
a, b =  legs of a right-triangle
c = length of hypotenuse

Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 +   S^2+4S+4  = 100 cm^2   [collect terms and isolate]
2S^2+4S =  100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0   means (S+8)=0, S=-8
or                                   (S-6)=0, S=6
Reject nengative root, so
Shorter leg = 6 cm
Longer leg = 6+2 cm = 8 cm
Hypotenuse (given) = 10 cm