A carpenter wants to be sure that the corner of a building is square and measures 6.0 ft and 8.0 ft along
the sides. How long should the diagonal be?
A. 12 ft
B. 10 ft
C. 11 ft
D. 14 ft
sqrt ( 6 ^ 2 + 8 ^ 2 ) =
sqrt ( 36 + 64 ) =
sqrt ( 100 ) = 10 ft
This is time for the Pythagorean Theorem.
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
10 = c
To find the diagonal length of the building, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the building form a right angle, so we can consider one side as the base and the other side as the height of the right triangle.
Given that the length of one side is 6.0 ft (let's call it side A) and the other side is 8.0 ft (let's call it side B), we can calculate the length of the diagonal (let's call it D) using the Pythagorean theorem:
D^2 = A^2 + B^2
D^2 = 6.0^2 + 8.0^2
D^2 = 36.0 + 64.0
D^2 = 100.0
To find the actual length of the diagonal, we take the square root of both sides:
D = √100.0
D = 10.0 ft
Therefore, the correct answer is B. The length of the diagonal should be 10 ft.