Find the area of a right-angled triangle if the radius of its circumcircle is 2.5 cm and the altitude drawn to the hypotenuse is 2 cm long.

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cm 2

cm 2

cm 2

cm 2

answer is A.

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Detailed Solution

Given that the radius of a circumference of right triangle and altitude drawn to the hypotenuse are given as

cm and

cm.
We have to find the area of the right-angled triangle.
The expression to find the area of a triangle is

A = 12 b h

.Here b and h are the base and height of a triangle.
The required figure geometry is shown below,
Question Image

In the right triangle, the hypotenuse is the diameter of the circumcircle and its center is the mid-point of the hypotenuse. So,
Question Image

Then, the area, A of a triangle ACB is, Question Image

The area is

5 cm 2

.
Therefore, the correct option is 1.

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