The art club wants to paint a rectangle-shaped mural to celebrate the winners of the track and field meet. they design a checkerboard background for the mural where they will write the winners’ names. the rectangle measures 432 inches in length and 360 inches in width. apply euclid’s algorithm to determine the side length of the largest square they can use to fill the checkerboard pattern completely without overlap or gaps.

72 inches

Step-by-step explanation:

We are given that

Length of rectangle=423 inches

Width of rectangle=360 inches

We have to find the side length of the largest square they can use to fill the checkboard pattern completely without overlap or gaps with the help of Euclid's algorithm.

In order to find the largest side of square we will find HCF (432,360).

Euclid's algorithm

a=dividend

b=divisor

q=quotient

r=remainder

a=432,b=360

HCF(432,360)=72

Hence, the side of largest square=72  inches