Answer:
Hypotenuse = 5 in
Longer leg = 4 in
Shorter leg = 3 in
Step-by-step explanation
The longer leg = x
The shorter leg = x - 1
Now through Pythagoras theorem:
hyp^2 = leg1^2 + leg2^2
5^2 = x^2 + (x - 1)^2
25 = x^2 + x^2 - 2 x + 1^2
25 = 2 x^2 - 2 x + 1
2 x^2 - 2 x - 24 = 0
2 ( x^2 - x - 12) = 0
2 (x - 4) (x + 3) =0
then x = 4 or x = - 3
We use the positive answer since we are looking for a length
then longer leg is 4 inches long,
and therefore the shorter one is one inch shorter than 4 in . That is:
shorter leg = 3 inches
