Answer
12, 16
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+4
leg c=20
(x)^2+(x+4)^2=400
x^2+x^2+8x+16=400
2x^2+8x+16=400
Factor
2(x^2+8x+16=400)
x^2+4x+8=200
Simplify
x^2+4x-192=0
Using ac method a=-192 b=4
Find two numbers that their products are -192 and their sums are 4. These two numbers are 16 and -12. Rewrite:
x^2+16x-12x-192=0
x(x+16)-12(x+16)=0
(x-12)(x+16)=0
x-12=0 x=12
x+16=0 x=-16 a negative length does not make sense.
So leg a=x a=12
leg b=x+4 b=12+4 b=16
leg c=20
proof (12)^2+(16)^2=(20)^2
144+176=400
