Answer:
Using Pythagoras theorem:
[tex]\text{Hypotenuse side}^2 = \text{Opposite side}^2+ \text{Adjacent side}^2[/tex]
As per the statement:
From the given diagram:
In a rt. triangle FGH we have;
Opposite side=FH = 35 units ,
Adjacent side = FG = r units and
Hypotenuse side= GH = 25+r units
Apply the Pythagoras in FGH to solve for r:
[tex](25+r)^2 = 35^2+r^2[/tex]
⇒[tex]625+r^2+50r = 1225+r^2[/tex]
or we can write this as:
⇒[tex]625+50r = 1225[/tex]
Subtract 625 from both sides we have;
⇒[tex]50r =600[/tex]
Divide both sides by 50 we have;
r = 12 units
Therefore, the length of the radius r is, 12 units
