Answer:
45
Step-by-step explanation:
Let the length of the shorter leg be represented as x.
Let the length of the longer let let be represented as x+15
While the length of the hypotenuse be 2x-15.
From the knowledge of phythagoras theorem:
x^2+(x+15)^2 = (2x-15)^2
x^2+x^2+15x+15x+225 = 4x^2-30x-30x+225
2x^2+30x+225 = 4x^2-60x+225
2x^2-4x^2+30x+60x+225-225=0
-2x^2+90x+0= 0
2x^2-90x = 0
Divide through by 2
x^2-45x=0
x(x-45)=0
x = 0 or x-45=0
Considering x-45=0
x-45=0
x = 45
If x is for the shorter leg,
The length for the longer leg is: x+15
= 45+15
= 60
For the hypotenuse = 2x-15
= 2×45-15
= 90-15
= 75
