Question

10. A door frame that appears rectangular has height 80 in., width 32 in., and one diagonal that measures 86 in. Is the door frame actually rectangular? Explain.

Answer 1

In a rectangle, the opposite sides are equal. The diagonal connects the opposite ends of the rectangle. This means that a right angle triangle can be formed as shown in the diagram below

Looking at the door frame above, we would confirm if it is actually a rectangle by applying pythagoras theorem which is expressed as

Hypotenuse^2 = opposite side^2 + adjacent side^2

It becomes

86^ = 80^2 + 32^2

7396 = 6400 + 1024

7396 is not equal to 7424

We can see that pythagoras theorem was not obeyed. Therefore,

The door frame is not a rectangle