Solve for the measure of one diagonal in a rectangle with sides of length 20m and 32m. (Round to the nearest tenths place)
Understand the Problem
The question asks to find the length of the diagonal of a rectangle, given the lengths of its two sides. This can be solved using the Pythagorean theorem.
Answer
$37.7$
Answer for screen readers
$37.7$
Steps to Solve
- Identify the sides of the rectangle
The sides of the rectangle are given as 20 m and 32 m. These will be the legs of the right triangle formed by the diagonal.
- Apply 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 lengths of the other two sides. In this case, the diagonal is the hypotenuse, and the sides of the rectangle are the other two sides. The formula is expressed as:
$$a^2 + b^2 = c^2$$
where $a$ and $b$ are the lengths of the sides, and $c$ is the length of the diagonal (hypotenuse). Substitute $a = 20$ and $b = 32$ into the formula:
$$20^2 + 32^2 = c^2$$
- Calculate the squares of the sides
$$20^2 = 400$$
$$32^2 = 1024$$
- Add the squares
Substitute the squared values back into the equation:
$$400 + 1024 = c^2$$
$$1424 = c^2$$
- Solve for $c$ (the length of the diagonal)
Take the square root of both sides of the equation:
$$c = \sqrt{1424}$$
$$c \approx 37.7359$$
- Round to the nearest tenths place
Round the result to one decimal place:
$$c \approx 37.7$$
$37.7$
More Information
The diagonal of the rectangle is approximately 37.7 meters. This is found using the Pythagorean theorem, which relates the sides of a right triangle to its hypotenuse.
Tips
A common mistake is to forget to take the square root after summing the squares of the sides. Another mistake is incorrect rounding.
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