Question

The area of the circumcircle of the right angle triangle is 154sq cm. Write the length of the greater side of the triangle?


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Answer 1

Answer:

For a right angled triangle with sides a,b anc c units, the area = 1/2 x product of perpendicular sides = abc/4R.

(Where, R = Circumradius of the Right angled triangle).

Now in the given question, the perpendicular sides are 8 and 4√5 units.

Thus, 1/2 x (8 x 4√5) = (8 x 4√5 x 12)/4R

OR R = 12/2 = 6cm.

Thus, area of the circumcircle => πR²

= π x (6²)

= 36π sq cm.

Approach 2: (The shortcut !)

Concept : The circumradius (R) of a right angled triangle = (Hypotenuse)/2.

Here, the largest side i.e. the hypotenuse = 12 cm.

Thus, the circumradius (R) = 12/2 = 6cm.

Thus, area of the circumcircle =>πR²

= π x (6²)

= 36π sq cm.

Step-by-step explanation:

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