Math CentralQuandaries & Queries


Question from Cordilla, a parent:

the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a 'let statement'.

We have two responses for you

Hi Cordilla.

Start with "Let a equal the length of the shortest side"

then explain what the length of the middle and longest sides are in algebraic terms.

The perimeter is the sum of the three side lengths, so if you add the algebraic forms for each side together, you get 102 meters. That's an equation and you can solve for a to finish the solution.

Stephen La Rocque.


Hi Cordilla,

To use algebra to solve this question you let a letter stand for the length of one of the sides. You need to decide which side you are going to represent and what letter to use. The "let statement" tells the reader what your choices are. Stephen decided to use the letter a and have it represent the length of the shortest of the three sides. hence he said "Let a equal the length of the shortest side." From this he is then able to write an equation for a. You could just as easily have decided to use a different latter, say b, and have it represent the length of the longest side. The statement would then be "Let b equal the length of the longest side." This would allow you to set up an equation for b. The choice is yours.

I hope this helps,

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