Expert: Scott A Wilson - 3/14/2010

Question
The question out of the book is..

The perimeter of a triangle is 51cm. The longest side is twice the length of the shortest side. The third side is 3cm longer than the shortest side. How long is each side? write an equation that represents the problem and then solve it.


thank you for any help.

Answer
Any triangle has three sides, A, B, and C.

They are labeled so that A is the longest, B is the shortet, and C is in between.
The perimeter is 51, which is the sum of the sides.  So we have A + B + C = 51.

The longest side is A, and the shortest side is B, so A = 2B.
The 3rd side is 3cm less than the longest side, so C + 3 = A.

Thus, we have to solve the equations
A + B + C = 51, A = 2B, and C + 3 = A.

Since A = 2B, that can be put in, giving 3B + C = 51 and C + 3 = 2B.

Subtract what the other factors from the left side of both equations to get C = ....

Since C is equal to both of them, set them equal and solve for B.

Once B has been found, solve for C using C = 2B - 3 and solve for A using A = 2B.

The other equations should be checked to make sure it was done correctly.