An angle bisector of a triangle divides the opposite side of the triangle into segments 5 cm and 3 cm long. a second side of the triangle is 7.6 cm long. find the longest and shortest possible lengths of the third side of the triangle. round answers to the nearest tenth of a centimeter.

Longest possible length of III side of triangle =12.7cm

shortest possible length of III side of triangle =4.6cm .

Step-by-step explanation:

Given , an angle bisector of triangle divides the opposite side of triangle into segments 5cm and 3cm long.

In figure I

 AB=a, BD=5cm , DC=3cm  AC=b

If AB is second side Then AB=7.6cm

Third side=AC=b

Now, by angle bisector theorem

a=7.6 cm

By cross multiply we get

b=4.6cm

III side of triangle =4.6cm

In II figure

we take II side AB=a=7.6 cm

III side=b

Again , by using bisector angle theorem

By cross multiply

b=12.7 cm

Hence, the longest possible length of  III side of triangle =12.7cm

 the shortest possible length of III side of triangle =4.6 cm

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