SOLUTION: Kindly please answer this question and thank you in advance: In triangle ABC, AB is 9 cm. shorter than AC, while BC is 3 cm. longer than AC. If the perimeter of the triangle i

Algebra ->  Equations -> SOLUTION: Kindly please answer this question and thank you in advance: In triangle ABC, AB is 9 cm. shorter than AC, while BC is 3 cm. longer than AC. If the perimeter of the triangle i      Log On


   

Question 107075: Kindly please answer this question and thank you in advance:

In triangle ABC, AB is 9 cm. shorter than AC, while BC is 3 cm. longer than AC. If the perimeter of the triangle is 48 cm. find the lengths of the three sides.
Answer by blueskyy(3) About Me  (Show Source):
You can put this solution on YOUR website!

Let the length of AC = L
so, AB = L-9( since AB is 9 cm shorter than AC)
and BC = L+3( since BC is 3cm longer than AC)
Let the perimeter = P = 48

so, AC + AB + BC = 48
or L+(L-9)+(L+3)= 48
OR L + L - 9 +L + 3 = 48
OR 3L - 9 + 3 = 48
OR 3L - 6 = 48

OR 3L = 48 + 6
OR 3L = 54
OR L = 54 / 3
OR L = 18
SO, AC = 18
SO AB = AC - 9
= 18 - 9
= 9
AND BC = AC + 3
= 18 + 3
= 21
CHECK :
AC + BC + AB = 18 + 9 + 21
= 48