A rectangle with a length of 32 untis and a width of 18 units; find the length of a diagonal.
Use the Pythagorean Theorem:
a^2 = b^2 = c^2
c = diagonal/hypotenuse
Or, for those of us with a "+" key,
a^2 + b^2 = c^2
:-)
To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the case of a rectangle, the diagonal acts as the hypotenuse of a right triangle formed by the length and width of the rectangle. The squares of the length (32 units) and width (18 units) are the other two sides.
So, we can use the formula:
diagonal^2 = length^2 + width^2
Substituting in the given values:
diagonal^2 = 32^2 + 18^2
Calculating this equation:
diagonal^2 = 1024 + 324
diagonal^2 = 1348
To find the length of the diagonal, we need to take the square root of both sides:
diagonal = √1348
Using a calculator, we find:
diagonal ≈ 36.73 units
Therefore, the length of the diagonal of the rectangle is approximately 36.73 units.