Based in the information given in the problem, you must apply the The Angle Bisector Theorem. Let's call the triangle: "ABC"; the internal bisector of the angle that divides its opposite side: "AP"; and "x": the longest and shortest possible lengths of the third side of the triangle.

If BP= 6 cm and CP= 5 cm, we have:

BP/CP = AB/AC

We don't know if second side of the triangle (6.9 centimeters long) is AB or AC, so:

1. If AB = 6.9 cm and AC = x:
6/5 = 6.9/x
x = (5x6.9)/6
x = 5.80 cm

2. If AC= 6.9 cm and AB= x:
6/5 = x/6.9
x = 6.9x6/5
x = 8.30 cm

Then, the answer is:
The longest possible length of the third side of the triangle is 8.30 cm and the and shortest length of it is 5.80 cm.

6 0

3 years ago

A price is decreased from £800 to £640. Calculate the percentage change.

Anni [7]

There is a decrease of 20% from ÂŁ800 to ÂŁ640.

A change from 800 to 640 represents a negative change (decrease) of -20% Using the formula :

Percent change = [(800 - 640) / 800] x 100 = -20 % (decrease)

800 is the old value and 640 is the new value. In this case we have a negative change (decrease) of -20 percent because the new value is smaller than the old value.

6 0

3 years ago

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