Answer:
a=24
b=10
c=26
Step-by-step explanation:
Perimeter is the sum of the sides ([tex]a+b+c=60[/tex])
The legs (a and b) have a ratio of 5:12, which means that [tex]5a=12b[/tex], which can be simplified to [tex]\frac{5}{12} a=b[/tex], where b will be the smaller leg.
The hypotenuse will be double the smallest leg, 2b, increased by 6 meters, giving us an equation of [tex]c=2b+6[/tex]
Let's plug these in to get one variable:
[tex]a+b+c=60\\a+b+2b+6=60\\a+\frac{5}{12}a+2(\frac{5}{12}a)+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a=54\\\frac{27a}{12}=54\\27a=648\\a=24[/tex]
Now that we have a, we can plug it in to our previous equations to find our other sides:
[tex]5a=12b\\5(24)=12b\\120=12b\\10=b[/tex]
[tex]c=2b+6\\c=2(10)+6\\c=20+6\\c=26[/tex]
Double-checking:
[tex]a+b+c=60\\24+10+26=60\\60=60[/tex]
