The length of a rectangle is 7 units and its width is 5 units. What is the approximate length of the diagonal of the rectangle?
A. 4.9 units
B. 6 units
C. 8.6 units
D. 9 units
ZXCV
To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the length and width of the rectangle make up the two sides of a right triangle, and the length of the diagonal is the hypotenuse. Let's call the length of the rectangle "a" and the width "b".
Using the Pythagorean theorem, we have:
diagonal^2 = length^2 + width^2
Plugging in the given values, we get:
diagonal^2 = 7^2 + 5^2
diagonal^2 = 49 + 25
diagonal^2 = 74
To find the approximate length of the diagonal, we need to take the square root of both sides:
diagonal = sqrt(74)
The approximate length of the diagonal is the square root of 74.
Now, let's calculate the value:
sqrt(74) ≈ 8.6
So, the approximate length of the diagonal of the rectangle is 8.6 units.
Therefore, the correct answer is C. 8.6 units.
49 + 25 = 74
What is the square root of 74?