a square foot tile has a decorative line connected the diagonal corners. If the sides of the tile are 12 inches, what is the length of the diagonal to the nearest tenth?
a^2 + b^2 = c^2
12^2 + 12^2 = c^2
144 + 144 = c^2
288 = c^2
17 = c
To find the length of the diagonal of the square tile, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square 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 two sides of the square tile are equal and measure 12 inches each. Let's label one side as "a" and the diagonal as "d".
Using the Pythagorean theorem, we can set up the equation:
a² + a² = d²
Simplifying the equation:
2a² = d²
Now we can substitute the value of "a" into the equation:
2(12²) = d²
2(144) = d²
288 = d²
To find the length of the diagonal, we need to take the square root of both sides of the equation:
√288 = √(d²)
Taking the square root:
d ≈ 16.97
Therefore, the length of the diagonal of the square tile is approximately 16.97 inches to the nearest tenth.
To find the length of the diagonal of a square tile, we can utilize the Pythagorean Theorem. This theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the square tile are given as 12 inches each. Let's label one of the sides as "a" and the other side as "b." The diagonal is the hypotenuse, which we will label as "c."
According to the Pythagorean Theorem, we have:
c^2 = a^2 + b^2
Substituting the given values, we get:
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
To find the value of c, we take the square root of both sides:
c = √288
Using a calculator, the square root of 288 is approximately 16.9706.
Rounding this value to the nearest tenth, we get the length of the diagonal as 16.9 inches.