Question

A person makes a mistake when copying information regarding a particular triangle. The copied information is as follows: Two sides of a triangle are the same length. The third side is 10 feet less than three times the length of one of the other sides. The perimeter of the triangle is 5 feet. What is the mistake?

Answer 1

No such triangle can exist. Any of the described relations may be in error.

Explanation:

Taken at face value, the sum of the lengths of the sides is ...

x + x + (3x-10) = 5

5x = 15

x = 3

so the third side is 3·3 -10 = -1 in length. No such triangle can exist.

If one side is actually 3x-10, the perimeter must be greater than 6 2/3 and less than 40.

If the perimeter is actually 5, then the third side must be 3x-7.5 or an expression with an even smaller constant.

So, the mistake could be in copying any of the numbers, or in copying the multiplier in the description of the 3rd side. There is insufficient information to tell exactly what the mistake is.