Question

Maria looks at the architectural plan of a four-walled room in which the walls meet each other at right angles. The length of one wall in the plan is 13 inches. The length of the diagonal of the floor of the room in the plan is approximately 15.26 inches. Is the room in the shape of a square?

Answer 1

No, the room is not square.

Explanation:

Pythagoras taught us that:

`a^(2) + b^(2) = c^(2)`

So if the room was square, then a would equal b, and if we squared 13 twice and added those together, then the square root of that would equal the 15.26" they gave us. Let's see if it does:

`c^(2) =` 13² + 13² = 169 + 169 = 338

To find c, take the square root of both sides:

c = 18.38

And that's NOT equal to 15.26", so the room is NOT a square.

A quicker way to do this would be to remember the side lengths of a 45/45/90 triangle: 1/1/
`√(2)` (Because the sides are equal, that makes it half of a square, and the hypotenuse is the diagonal of that square.)

`√(2)` = 1.414, so if we multiplied that by the length of "one wall," 13", we'd get 15.26" if the room was square:

1.414 x 13 = 18.38

That's the same answer as before, and since the 15.26" they gave us doesn't match that, the room isn't square.

Bonus: knowing the length of one wall and the diagonal, can you calculate the length of the other wall?