Answer :
The radius of table can be 13 inches or 73 inches.
Let r inches be the table's radius.
Make the corner the starting point or origin.
the coordinates for the table's center are as follows: (r, r).
So [tex](x-r)^{2} +(y-r)^{2}=r^{2}[/tex] is the equation for the table's diameter.
The distance between the mark at the table's edge and one wall is 18 inches and 25 inches, respectively. Consequently, this point's coordinates are (18, 25). It might alternatively be (25, 18), but our calculations would not be affected.
Given that the mark is on the edge, it satisfies the criteria established by the table's circumference equation.
[tex](18-r)^{2} +(25-r)^{2} =x^{2}[/tex]
[tex]324-36r+r^{2} +625-50r+x^{2} =x^{2}[/tex]
[tex]r^{2} -86r+949=0[/tex]
(r−13)(r−73)=0
r=13 inches or r=73 inches
As a result, the table's radius can be either 13 inches or 73 inches.
To learn more about radius here:
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