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