Answer
9, 12
Work Step by Step
Based on Pythagorean theorem a^2 +b^2 = c^2 where a and b are the equal legs and c is the hypotenuse.
leg a=x
leg b=x-3
leg c=15
(x)^2+(x-3)^2=225
x^2+x^2-6x+9=225
2x^2-6x+9-225=0
Simplify
2x^2-6x-216=0
Using ac method a=-432 b=-6
Find two numbers that their products are -432 and their sums are -6. These two numbers are 18 and -24. Rewrite:
2x^2+18x-24x-216=0
2x(x+9)-24(x+9)=0
(2x-24)(x+9)=0
2x-24=0 2x=24 x=12
x+9=0 x=-9 a negative length does not make sense.
So leg a=x a=12
leg b=x-3 b=12-3 b=9
leg c=15
proof (12)^2+(9)^2=(15)^2
144+81=225
