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erastovalidia [21]
2 years ago
10

An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the

triangle is 6.9 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.
Mathematics
1 answer:
sveticcg [70]2 years ago
6 0
<span>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.</span>


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Answer:

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1. 10×12+8×10+8×13+8×15

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What is the sum of the finite arithmetic series (-5)+0+5+10+ ......+65
Alex17521 [72]

If you want to solve this problem using formulas, there are two important formulas:

t1  =  first term  =  -5          

tn  =  nth term  =  last term  =  -5

n  =  numbr of terms

Sn  =  sum of the n terms

tn  =  t1 + (n - 1)d     --->     65  =  -5 + (n - 1)(5)

                                          65  =  -5 + 5n - 5

                                          65  =  -10 + 5n

                                          75  =  5n

                                            n  =  15

Sn  =  n(t1 + tn)/2     --->     Sn  =  15(-5 + 65)/2

                                          Sn  =  450


So ur answer rounds up to 450


Letter c

:)

hope i helped 


~Luis

5 0
3 years ago
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