The perimeter of a triangle is 69 cm. the measure of the shortest side is 5 cm less than the middle side. the measure of the longest side is 5 cm less than the sum of the other two sides. find the lengths of the sides.
a. 17 cm; 21 cm; 31 cm
b. 15 cm; 21 cm; 33 cm
c. 16 cm; 21 cm; 32 cm
d. 15 cm; 22 cm; 32 cm

option C

Step-by-step explanation:

We will call:

a= the shortest side

b= the middle side

c = the longest side

perimeter= p =69cm

So we have:

69 = a+b+c      equation 1

a= b-5             equation 2

c= a+b-5         equation 3

Using equation 1 we have:

69-c = a+b

Using equation 3 we have:

c+5=a+b    

we substitute equation 1 in equation 3:

c+5=69-c

2c=64    

c=64/2   so we have c =32cm

Using: c+5=a+b

32+5=a+b

37=a+b    

a=37-b

Using equation 2 we have:

37-b=b-5

37+5=2b

42/2=b   we have b=21cm

a=37-b=37-21= 16 cm  

Finally: a=16 cm    b=21 cm    c=32cm

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step-by-step explanation: