Question

The perimeter of a triangle is 39 inches. The second side is 9 times as long as the first side. The third side is 1 inch longer than the second side. Find

the length of each side.

Answer 1

First side: 2 in

Second side: 18 in

Third side: 19 in

Explanation:

Let's first side be x

then second side = 9x and

third side = 9x + 1

Then you put all of than in a equation

x + 9x + 9x + 1 = 39

Simplify by combining like terms 9x+9x=18x+x=19x+1=39

19x+1=39

Subtract 1 from both sides 39-1=38

19x=38

Divide both sides by 19 (38÷19=2)

X=2

Now we know that 2 is our first side lets subsitute x for 2

First side: 2in

Second side: 18in 9x → 9(2)=18in

The second side is 9 times the first side

Third side: 19in 1+9x → 1+9(2)=1+18=19in

The third side is 1 inch more than the second side

Answer 2

perimiter=x+y+z
x is 9 times as long as y
z is 1 longer than x

translate
x=9 times y or x=9y
z=1+x
subsitute 9y for x in the z=1+x equation
z=1+9y
subsitute z=1+9y and x=9y in the equation
9y+y+1+9y=39
add like terms
19y+1=39
subtract 1 from both sides
19y=38
divide by 19
y=2
subsitute
x=9y
x=9(2)
x=18

z=1+9y
z=1+9(2)
z=1+18
z=19

the side legnths are
first side: 2 in
second side: 18 in
third side: 19 in