An artist is creating a sculpture using bendable metal
rods of equal length. one rod is formed into the
shape of a square and another rod into the shape of
an equilateral triangle. if each side of the triangle is
2 inches longer than each side of the square, how
long, in inches, is each rod?
a) 16
b) 18
c) 24
d) 30
( explain and show your work )

Option C 24 in

Step-by-step explanation:

Let

x> the length of each rod

b > the length side of the square

a > the length side of the equilateral triangle

we know that

The perimeter of the square is 4b

The perimeter of equilateral triangle is 3a

so

2x=4b+3a > equation A

4b=3a > equation B

a=b+2 > equation C

Substitute equation C in equation B and solve for b

4b=3(b+2)

4b=3b+6

4b-3b=6

b=6 in

Find the value of a

a=b+2 > a=6+2=8 in

Find the value of x

x=4b  or x=3a

x=4(6)=24 in

therefore

The length of each rod is 24 inches

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b