Linear Equation word problems

Question

The length of an isosceles triangle is one fourth the length of its legs. If the perimeter of the triangle is 14 inches. What is the length of the base?

Answer 1

When possible, assign a variable to the value the problem asks you to find (so you won't forget to solve for it at the end).  Here, let x = length of base.

 

The length of the base (x) is (1/4)(length of leg).  That means length of a leg is 4x.

 

The perimeter is the length of the base + 2(length of a leg)

     14 inches    =       x                        + 2(4x)

          14 = 9x                (collecting terms)

           x = 14/9 inches

Answer 2

Hi Chris

 

An isosceles triangle is one in which 2 sides (legs) are the same length and the base is a different length.  So when you say the length of an isosceles triangle is 1/4th the length of the legs I assume you mean the base length is 1/4th the length of one of the legs.   You know 3 things about your triangle;

 

1. The 2 legs are the same length, let's call that length X

2. The base is 14th the length of the leg so the base is 1/4 * X

3. The perimeter of the triangle is 14 inches.

 

As I am sure you know, the perimeter is the measure of all 3 lengths, the base and 2 legs so let's set up that equation:

 

X + X + 1/4*X = 14

 

Now solve algebraically for X

 

2X + 1/4X = 14

9/4X = 14

X = 56/9

 

The base is 1/4 of this number so 1/4 * 56/9 = 14/9

 

Please let me know if this is the right answer for you

 

All the best 

 

Lori