If the radius of its circumcircle is 5 cm and the altitude drawn to the hypotenuse is 4 cm, the area of a right-angled triangle is equal to_________.

Asked by gpnkumar0 | 5th Aug, 2016, 06:10: PM

Expert Answer:

begin mathsize 20px style Given colon space The space radius space of space circumcircle space of space straight a space triangle space is space 5 space cm space and space its space altitude space drawn space to space the space
hypotenuse space is space 4 space cm.
This space implies space that space the space triangle space is space straight a space right space angled space triangle.
rightwards double arrow The space hypotenuse space is space the space diameter space of space the space circle.... left parenthesis Since space if space an space angle space of space straight a space triangle space is space 90 degree comma space the space hypotenuse space of space that space triangle space will space
be space the space diamter space of space the space triangle right parenthesis
So comma space hypotenuse equals diameter space of space the space circle equals 2 space radius equals 2 space left parenthesis 5 right parenthesis equals 10 space cm
Area space of space the space triangle equals 1 half cross times base space cross times height equals 1 half cross times 10 cross times 4 equals 20 space cm squared
So comma space area space of space straight a space right minus angled space triangle space is space 20 space cm squared. end style

Answered by Rebecca Fernandes | 7th Aug, 2016, 10:32: AM