geometry
posted by verenice on .
the legs of a right angled triangle are 5 cm and 12cm long. find the lengths, to the tenth, of the segment into which the bisector of the right angle divides the hypotenuse.

Let ABC be the rightangled triangle with angleB = 90°
let the bisector angle B be BD where D is on the hypotenuse AC
We know that AD : DC = areaABD : areaBCD
areaABD = (1/2)(12)(BD)sin45°
areaBCD = (1/2)(5)(BD)sin45°
then areaABD : areaBCD = 12 : 5
so AD = (12/17)(13) = 9.2
and DC = 139.2 = 3.8