help me plz

Question

in a triangle in which the sides have different lengths the length of the shorter side is 5 less then the length of the next longest side. The length of the longest side of the triangle is 1 more than three times the length of the shortest side.If the perimeter of the triangle is 21 what are the lengths of the three sides of the trianle

Answer 1

let's call the length of the shortest side "S", the next side M for Medium, and the longest L.

 

The first sentence translates to 

 

M = S + 5

 

The second sentence translates to 

 

L = 3*S + 1 

 

The third sentence translates to 

 

S + M + L = 21

 

Now, substitute the first two sentences into the third and you get 

 

S + (S + 5) + (3S +1) = 21

 

gather all hte S's together and count em up.

 

(S + S + 3*S) + (5 + 1) = 21

5*S + 6 = 21

5*S =21 - 6 = 15 

 

S = 15/5 = 3

 

So the shortest side is 3 long.  Now substitute that into the other formulae, to get

 

M = S + 5 = 3 + 5 = 8

 

L = 3*S + 1 = 3* 3 + 1 = 9 + 1 = 10

 

and now check the perimeter

 

3 + 8 + 10 = 21 check

 

Answer 2

Let a, b, c be the lengths of the sides from shortest (a) to longest (c):

 

the perimeter of the triangle is 21:  21 = a + b + c

 

the length of the shorter side is 5 less then the length of the next longest side:  a = b-5

 

The length of the longest side of the triangle is 1 more than three times the length of the shortest side:  c = 3a + 1

 

21 = a + b + c

21 = (b-5) + b + (3a+1)           {Substitute b-5 for a and 3a+1 for c}

21 = (b-5) + b + 3(b-5) + 1      {Substitute b-5 for the remaining a}

21 = 5b - 19

40 = 5b

 

8 = b

 

a = b-5 = 8 - 5 = 3

 

c = 3a + 1 = 3*3 + 1 = 10

 

Check:

Perimeter = 21 = a + b + c

21 = 3 + 8 + 10

21 = 21

Check!