Question

the floor of a rectangular living room is 16 feet by 12 feet. what is the distance between opposite corners of the living room? feet

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the length and width of the rectangle are the legs, and the diagonal (distance between opposite corners) is the hypotenuse. We use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 16\), \(b = 12\), and \(c\) is the diagonal.

Step2: Apply the Pythagorean theorem

Substitute \(a = 16\) and \(b = 12\) into the formula: \(16^2 + 12^2 = c^2\). Calculate \(16^2 = 256\) and \(12^2 = 144\). Then \(256 + 144 = c^2\), so \(400 = c^2\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c = \sqrt{400} = 20\).

Answer:

20