What is the highest possible area of a right triangle whose circumradius is 3 cm (in cm2)?
Explanation:
In a right triangle circumradius is half of the hypotenuse.
∴ Hypotenuse of the triangle = 2 × 3 = 6 cm.
Area = ½ × hypotenuse × (altitude on hypotenuse) = ½ × 6 × (altitude on hypotenuse)
Now, the area will be highest when altitude on the hypotenuse is highest.
⇒ The highest value of hypotenuse will be equal to circumradius i.e., 3 cm.
∴ Highest possible area = ½ × 6 × 3 = 9 cm2.
Hence, option (a).
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