the perimeter of tright triangle is 60 cm and its hypotenuse is 25cm. find the are if the triangle.

Asked by pereiracalida | 28th Sep, 2017, 09:15: PM

Expert Answer:

begin mathsize 16px style Let space the space base space of space straight a space right minus angled space triangle space be space straight b space and space height space be space straight h.
Hypotenuse equals 25 space cm
Now comma space perimeter space of space straight a space triangle equals 60 space cm
rightwards double arrow straight b plus straight h plus 25 equals 60
rightwards double arrow straight b plus straight h equals 35
rightwards double arrow left parenthesis straight b plus straight h right parenthesis squared equals 35 squared
Also comma space straight b squared plus straight h squared equals 25 squared
Now comma
open parentheses straight b plus straight h close parentheses squared minus open parentheses straight b squared plus straight h squared close parentheses equals 35 squared minus 25 squared
rightwards double arrow straight b squared plus straight h squared plus 2 bh minus straight b squared minus straight h squared equals left parenthesis 35 plus 25 right parenthesis left parenthesis 35 minus 25 right parenthesis
rightwards double arrow 2 bh equals 600
rightwards double arrow bh equals 300
Area space of space straight a space triangle equals 1 half cross times straight b cross times straight h equals 1 half cross times 300 equals 150 space cm squared end style

Answered by Rashmi Khot | 29th Sep, 2017, 10:56: AM