Question

8. A right triangle has a perimeter of 60 cm. The legs have a ratio of 5:12. The hypotenuse is twice the

Answer 1

Answer:

a=24

b=10

c=26

Step-by-step explanation:

Perimeter is the sum of the sides ($a+b+c=60$)

The legs (a and b) have a ratio of 5:12, which means that $5a=12b$, which can be simplified to $\frac{5}{12} a=b$, 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 $c=2b+6$

Let's plug these in to get one variable:

$a+b+c=60\\a+b+2b+6=60\\a+\frac{5}{12}a+2(\frac{5}{12}a)+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a+6=60\\\frac{12}{12}a+\frac{5}{12}a+\frac{10}{12}a=54\\\frac{27a}{12}=54\\27a=648\\a=24$

Now that we have a, we can plug it in to our previous equations to find our other sides:

$5a=12b\\5(24)=12b\\120=12b\\10=b$

$c=2b+6\\c=2(10)+6\\c=20+6\\c=26$

Double-checking:

$a+b+c=60\\24+10+26=60\\60=60$