Question

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 )

Answer 1

Option C 24 in

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