Which of the following shows the length of the third side, in inches, of the triangle below? (1 point)
A right triangle is shown. One side of the triangle is labeled as 25 inches. The height of the triangle is labeled as 15 inches.
20 inches
Square root of 850 inches
Square root of 10 inches
40 inches
In order to determine the length of the third side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
Let's label the two shorter sides as 'a' and 'b', and the hypotenuse as 'c'.
We are given that one side of the triangle is 25 inches and the height is 15 inches. So, 'a' = 15 inches and 'b' = 25 inches.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
15^2 + 25^2 = c^2
225 + 625 = c^2
850 = c^2
To find 'c', we take the square root of both sides:
c = √850
Therefore, the length of the third side of the triangle is the square root of 850 inches. The correct answer is "Square root of 850 inches".