Question

what is the length of the diagonal of the rectangle?

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem for a right - triangle (formed by the sides and diagonal of the rectangle) is \(a^{2}+b^{2}=c^{2}\), where \(a = 17\), \(b=12.75\), and \(c\) is the diagonal.
So, \(c=\sqrt{17^{2}+12.75^{2}}\).

Step2: Calculate squares

\(17^{2}=289\), \(12.75^{2}=(12 + 0.75)^{2}=12^{2}+2\times12\times0.75 + 0.75^{2}=144+18 + 0.5625=162.5625\).

Step3: Sum the squares

\(17^{2}+12.75^{2}=289+162.5625 = 451.5625\).

Step4: Take the square root

\(c=\sqrt{451.5625}\). Since \(21.25\times21.25=(20 + 1.25)^{2}=20^{2}+2\times20\times1.25+1.25^{2}=400 + 50+1.5625=451.5625\), so \(c = 21.25\).

Answer:

\(21.25\)