Question

find the length of the diagonal of the rectangle.
6
11
12
14
\sqrt{157}
\sqrt{174}

Explanation:

Step1: Apply the Pythagorean theorem

In a rectangle, the diagonal \(d\) forms a right - triangle with the length \(l = 11\) and the width \(w=6\). The Pythagorean theorem is \(d^{2}=l^{2}+w^{2}\).
Substitute \(l = 11\) and \(w = 6\) into the formula: \(d^{2}=11^{2}+6^{2}\).

Step2: Calculate \(l^{2}+w^{2}\)

\(11^{2}=121\) and \(6^{2}=36\). Then \(d^{2}=121 + 36\).
\(d^{2}=157\).

Step3: Solve for \(d\)

Take the square root of both sides. Since \(d>0\) (length of a diagonal), \(d=\sqrt{157}\).

Answer:

\(\sqrt{157}\)