Geometry problem help please

Question

My computer table has a square hole for a monitor. The diagonal of the hole (creating two 45-45-90 triangles) is 24 inches. Will a monitor measuring 18 inches by 12 inches fit? Justify your answer

Answer 1

First, let's write out what we know about 45-45-90 triangles. Each side of the triangle is the same and is equal to x and the diagonal or hypotenuse is equal to x√2. So to find the sides of the triangle (and the sides of the square), we need to figure out what x is.

 

we know the hypotenuse is 24. That tells us:

x√2=24

To get x alone, we divide both sides by √2.

x=(24√2)/2

x=12√2 which is approximately 16.97

 

Your computer hole is 16.97x16.97. A computer monitor that is 18x12 will not fit. 

 

Hope that helps,

Nikita

Answer 2

The hypotenuse of one of the 45-45-90 triangles is 24 inches, you're told. So, using special right triangles, divide 24 by √(2) to find the length of one of the hole's sides:

 

24/√(2) ≈ 16.97

 

Since the hole is a square, that means it's approximately 16.97 inches by 16.97 inches, which is not large enough for the monitor to fit.

 

 

You can also find the hole's side lengths using the Pythagorean Theorem, where both legs are length x (since they are equal):

 

c² = a² + b²

24² = x² + x²

576 = 2x²

288 = x²

16.97 = x