Question

triangle is 8 inch shorter than the side of a square. perimeter of the square is 46 inches more than the perimeter of the triangle. find the lengthof a side of the square

Answer 1

squares have equal length sides so 46/4 is the length of a side of the square = 11.5inches

Answer 2

first lets denote those things:
let s be the measue of the side of the square
let Pt be the perimeter of the triangle
let Ps be the perimeter of the square.

by saying that the triangle is 8 inch shorter than the side of a square, you mean perimeter of the triangle is 8 inch shorter than the side of a square
so:
Pt=s-8
now you also stated that the perimeter of the square is 46 inches more than the perimeter of the triangle which we can mathematically write as:
Ps=Pt+46
substituting s-8 to Pt
Ps=s-8+46
We know that the perimeter of a square is 4 times its side or simply Ps=4s. Substituting this....
4s=s-8+46
Now let's solve for s
4s=s-8+46
3s=38
s=38/3
s=12.666666666666666666666666666....inches
rounding off will give us
s=12.67 inches