The measures of a rectangle are 8 inches by 15 inches. Find the length of the diagonal.
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length and width of the rectangle are the two legs of the right triangle, and the diagonal is the hypotenuse.
Let's apply the Pythagorean theorem to find the length of the diagonal:
Length of the rectangle = 8 inches
Width of the rectangle = 15 inches
Using the Pythagorean theorem, we have:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = (8 inches)^2 + (15 inches)^2
Diagonal^2 = 64 square inches + 225 square inches
Diagonal^2 = 289 square inches
Taking the square root of both sides:
Diagonal = sqrt(289 square inches)
Diagonal = 17 inches
Therefore, the length of the diagonal of the rectangle is 17 inches.