Question

Is it possible to have a right triangle with sides measuring 7 inches, 10 inches, and 15 inches?

Short answer

Answer: No, the given side lengths cannot form a right triangle as they do not satisfy the Pythagorean theorem (7^2 + 10^2 ≠ 15^2).

Step-by-step solution

Identify the longest side

In this case, the longest side is 15 inches, which would be the hypotenuse if the triangle is a right triangle.

Apply the Pythagorean theorem

To check if the given measurements can form a right triangle, we need to see if the following equation holds true, where a and b are the two other sides and c is the hypotenuse (the longest side): a^2 + b^2 = c^2

Plug in the given side lengths

We will plug in the given side lengths to see if they satisfy the Pythagorean theorem: 7^2 + 10^2 = 15^2

Evaluate each side of the equation

Compute the square of each side length and calculate the left side and the right side of the equation: 49 + 100 = 225 149 (left side) != 225 (right side)

Compare the results

Since the sum of the squares of the two smaller sides (149) is not equal to the square of the longest side (225), the given side lengths cannot form a right triangle.