Question

4.2 - half a rectangle
score: 5/6 answered: 5/6
question 6
find x.
diagram of a square (or rectangle) with a diagonal, marked with x on one side, 44 on the diagonal, and tick marks indicating equal sides
x =
round your answer to the nearest two decimal places.
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Explanation:

Step1: Identify the shape and triangle properties

The figure is a square (since all sides are marked equal) with a diagonal of length 44. In a square, the diagonal \( d \) and side \( x \) are related by the Pythagorean theorem: \( d^{2}=x^{2}+x^{2}=2x^{2} \).

Step2: Solve for \( x \)

Given \( d = 44 \), substitute into the formula: \( 44^{2}=2x^{2} \). Calculate \( 44^{2}=1936 \), so \( 1936 = 2x^{2} \). Divide both sides by 2: \( x^{2}=\frac{1936}{2}=968 \). Take the square root: \( x=\sqrt{968}\approx31.11 \).

Answer:

\( 31.11 \)