What is the length of the diagonal of a rectangle that has a base of 16 and height of 12?
A) 18
B) 19
C) 20
D) 21
Answer (2)
The length of the diagonal of the rectangle is 20 units, calculated using the Pythagorean theorem. The formula used is d 2 = b 2 + h 2 . The correct answer is C) 20.
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Identifies the rectangle's base as 16 and height as 12.
Applies the Pythagorean theorem: d 2 = b 2 + h 2 .
Calculates d 2 = 1 6 2 + 1 2 2 = 256 + 144 = 400 .
Finds the diagonal length: d = 400 = 20 .
20
Explanation
Problem Analysis We are given a rectangle with a base of 16 and a height of 12. We need to find the length of the diagonal.
Applying Pythagorean Theorem Let the base of the rectangle be b = 16 . Let the height of the rectangle be h = 12 . Let the length of the diagonal be d . We can use the Pythagorean theorem to find the length of the diagonal: d 2 = b 2 + h 2 .
Calculations Substitute the given values: d 2 = 1 6 2 + 1 2 2 . Calculate 1 6 2 = 256 and 1 2 2 = 144 . So, d 2 = 256 + 144 = 400 .
Finding the Diagonal Length Take the square root of both sides: $d = 400 = 20 Therefore, the length of the diagonal is 20.
Final Answer The length of the diagonal of the rectangle is 20.
Examples
Understanding the diagonal of a rectangle is useful in many real-world scenarios. For example, when constructing a rectangular frame or laying out a garden, knowing the diagonal helps ensure the structure is square and stable. In sports, calculating the diagonal distance across a field can help athletes optimize their movements and strategies. This concept is also crucial in architecture and engineering for designing buildings and structures with precise dimensions and stability.
