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?

24 inches

Step-by-step 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=

Perimeter of equilateral triangle=

Using the above formula

Then , Length of square shaped rod=perimeter of square =

Perimeter of equilateral triangle =Length of equilateral shaped rod=

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

Length of each side of square =6 inches

Length of square shaped rod=

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

Length of equilateral shaped rod=

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

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