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A right triangle has side lengths 8, x, and x + 2. Which is the length of the hypotenuse?

User Richard Wolf
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1 Answer

20 votes
20 votes

Answer

8

Step-by-step explanation

The right triangle side lengths must satisfy the right triangle inequality which says that if a triangle has side lengths A, B, and C then the sum of any two side lengths must be greater than the measure of the third side


A+B>C

In our case, the side lengths 8, x, and x + 2 must satisfy this condition and therefore, we arrange the inequality such that the solution for x is a positive number (side lengths cannot be negative)

The right arrangement that satisfies the triangle inequality is


x+x+2>8

Let us solve for x to see which side length is the hypotenuse (the largest side length is the hypotenuse)

The left-hand side of the above inequality simplifies and gives us


2x+2>8

subtracting 2 from both sides gives


2x>6

Finally, dividing both sides by 2 gives


x>3

This means one side length is greater than 3, the other side length x + 2 is, therefore, greater than 5, and the third side length is 8.

Hence, the longest side length is 8, and therefore, it is the right answer.

User Daniel Calliess
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