Question

Linda is designing a circular piece of stained glass with a diameter of 7 inches. She is going to sketch a square inside the circular region.

What is the largest possible length of a side of the square (to the nearest tenth)?

Answer 1

(see attachment)
the diameter is the diaagonal of the squar which also makes a right triangle where the diagnal is the hypotnuse

and since it is a square
the legs are equal measure
a^2+b^2=c^2
where legs legnth a and b an hypotnuse legnth c
c=7
a=b
a^2+a^2=7^2
2a^2=49
divide by 2 both sides
a^2=19.5
sqrt both sides
a=√19.5

the legnth of 1 side is √19.5 max or aprox 4.41588 inches