Answer:
Diagonal Length = [tex]8\sqrt{10}[/tex] inches
Step-by-step explanation:
The suitcase is a rectangle with one side being 24 and another side being 8.
The diagonal is the line through the middle connecting two opposite corners.
If we draw the diagonal, it creates a triangle with one leg being 24 and another being 8.
The diagonal is the "hypotenuse" of the triangle.
Now, the pythagorean theorem:
leg^2 + another leg^2 = hypotenuse^2
So, we substitute the values known and find the hypotenuse (which is length of the diagonal). Shown below:
[tex]24^2+8^2=h^2\\640=h^2\\h=\sqrt{640}\\h=\sqrt{64*10}\\h=\sqrt{64}\sqrt{10}\\h=8\sqrt{10}[/tex]
We have written the answer in exact form (with radical in simplified term).
We also use the radical property [tex]\sqrt{a*b}=\sqrt{a}\sqrt{b}[/tex]
