round to the nearest tenth. a rectangular plot of land is 80 meters wide and 98 meters long. Find the length of the diagonal and if necessary, round to the nearest tenth.
This calls for the Pythagorean Theorem.
a^2 + b^2 = c^2
80^2 + 98^2 = c^2
6,400 + 9,604 = c^2
16,004 = c^2
126.506 = 126.5 = c
To find the length of the diagonal of the rectangular plot of land, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
In this case, one side of the right triangle is the width of the plot (80 meters) and the other side is the length of the plot (98 meters). Let's label the diagonal as "d," the width as "w," and the length as "l."
Using the Pythagorean theorem, we have the equation:
d^2 = w^2 + l^2
Substituting the given values, we get:
d^2 = 80^2 + 98^2
Simplifying this equation, we have:
d^2 = 6400 + 9604
d^2 = 16004
To find the length of the diagonal (d), we take the square root of both sides:
d = √16004
Calculating the square root of 16004, we find:
d ≈ 126.49
Rounding this to the nearest tenth, we get:
d ≈ 126.5 meters.
Therefore, the length of the diagonal is approximately 126.5 meters.