Question

question 5
find x.
diagram of a square with a right angle, all sides marked as equal (x), and a diagonal of 22
x =
round your answer to the nearest two decimal places.

Explanation:

Step1: Identify the figure

The figure is a square (all sides equal, right angle) with a diagonal of length 22. Let the side length be \( x \).

Step2: Apply Pythagorean theorem

In a square, the diagonal \( d \) and side \( x \) satisfy \( d^2 = x^2 + x^2 \) (since both legs are \( x \) in the right triangle formed by two sides and the diagonal). So \( d^2 = 2x^2 \).

Step3: Substitute \( d = 22 \)

We have \( 22^2 = 2x^2 \). Calculate \( 22^2 = 484 \), so \( 484 = 2x^2 \).

Step4: Solve for \( x^2 \)

Divide both sides by 2: \( x^2=\frac{484}{2}=242 \).

Step5: Solve for \( x \)

Take the square root: \( x = \sqrt{242} \approx 15.56 \) (rounded to two decimal places).

Answer:

\( x \approx 15.56 \)