Question

1. a window frame that appears to be rectangular has a height of 60 in, width of 11 in, and one diagonal that measures 61 in. is the window frame rectangular?

Explanation:

Step1: Recall Pythagorean theorem

For a rectangle, the diagonal \(d\), length \(l\), and width \(w\) satisfy \(d^{2}=l^{2} + w^{2}\). Here, height \(h = 60\) in (can be considered as length \(l\)) and width \(w=11\) in, diagonal \(d = 61\) in.
Calculate \(l^{2}+w^{2}\): \(60^{2}+11^{2}=3600 + 121=3721\)

Step2: Calculate \(d^{2}\)

Calculate \(d^{2}\) where \(d = 61\): \(61^{2}=3721\)

Step3: Compare the two results

Since \(60^{2}+11^{2}=61^{2}\), the triangle formed by the height, width, and diagonal is a right triangle. In a quadrilateral, if the diagonal forms a right triangle with the two adjacent sides, then the quadrilateral is a rectangle (because in a rectangle, all angles are right angles, so the diagonal splits it into two right triangles).

Answer:

Yes, the window frame is rectangular.