Question

h.o.t. problems higher order thinking

1. model with mathematics write a real - world problem that can be solved by using the pythagorean theorem. then explain how to solve the problem.

Explanation:

Let's consider a problem where we want to find the length of the diagonal of a rectangular garden. Suppose the length of the garden is \(a = 12\) meters and the width is \(b= 5\) meters. The Pythagorean Theorem \(c^{2}=a^{2}+b^{2}\) (where \(c\) is the length of the hypotenuse, which in this case is the diagonal of the rectangle) can be used.

First, we substitute the values of \(a\) and \(b\) into the formula: \(c^{2}=12^{2}+ 5^{2}\). Then we calculate \(12^{2}=144\) and \(5^{2}=25\). So \(c^{2}=144 + 25=169\). Taking the square root of both sides, \(c=\sqrt{169}\). Since \(\sqrt{169}=13\), the length of the diagonal is \(13\) meters.

Answer:

A real - world problem: "A rectangular garden has a length of 12 meters and a width of 5 meters. What is the length of its diagonal?"
Solution: Use the Pythagorean Theorem \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 12\) and \(b = 5\). Calculate \(c^{2}=12^{2}+5^{2}=144 + 25=169\). Then \(c=\sqrt{169}=13\) meters.