Question

the length of a rectangles diagonal is \\( \sqrt { 65 } \\), and the length of one of the rectangles sides is 4. what is the perimeter of the rectangle?
a. 11
b. 22
c. 28
d. 65

Explanation:

Step1: Find the other side length

Let the other side length be \(x\). Using the Pythagorean theorem (\(a^{2}+b^{2}=c^{2}\), where \(c\) is the diagonal and \(a = 4\), \(c=\sqrt{65}\)). So \(4^{2}+x^{2}=(\sqrt{65})^{2}\), which simplifies to \(16 + x^{2}=65\), then \(x^{2}=65 - 16=49\), and \(x = 7\).

Step2: Calculate the perimeter

The perimeter formula of a rectangle is \(P=2(a + b)\). Substituting \(a = 4\) and \(b = 7\), we get \(P=2(4 + 7)=2\times11 = 22\).

Answer:

B. 22