# geometry

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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.

• geometry -

Let ABC be the right-angled 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 = 13-9.2 = 3.8

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