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?

Answer 1

check the picture below.

so notice, their perimeter is the same, because the perimeter is just one rod anyway, and all rods are the same length, thus


`\bf P_s=P_t\implies 4s=3(s+2)\implies 4s=3s+6\implies s=6`

Answer 2

24 inches

Explanation:

We are given that an artist creating a sculpture using bendable metal rods of equal length.

One rod is in square shape and second rod is in equilateral triangle shape.

We have to find the length of each rod

Let side of square= x inches

Length of each side of equilateral triangle =x+2 inches

We know that perimeter of square=
`4* side`

Perimeter of equilateral triangle=
`3* side`

Using the above formula

Then , Length of square shaped rod=perimeter of square =
`4x`

Perimeter of equilateral triangle =Length of equilateral shaped rod=
`3(x+2)`

Length of square shaped rod=Length of equilateral triangle shaped rod

`4x=3(x+2)`

`4x=3x+6`

`4x-3x=6`

`x=6`

Length of each side of square =6 inches

Length of square shaped rod=
`4* 6=24 inches`

Length of each side of equilateral side=6+2=8 inches

Length of equilateral shaped rod=
`8* 3=24 inches`