Mr.perez is trying to move a circular folding table with a 4 foot radius through a window that measures 5 ft by 3 ft. He plans to lean the table over and move it through the diagonal of the window. Will the table go through the window?
With a 4 foot radius, the diameter is 8 feet.
a^2 + b^2 = c^2
5^2 + 3^2 = c^2
25 + 9 = c^2
34 = c^2
5.83 = c
So no?
That's right. The table with an 8 foot diameter won't fit in a space less than 6 feet long.
To determine whether the table will go through the window, we need to compare the size of the table with the available space in the window.
First, let's calculate the diagonal of the window using the Pythagorean theorem. The formula for finding the length of the diagonal (d) given the width (w) and height (h) of a rectangle is:
d = √(w^2 + h^2)
In this case, the width (w) of the window is 5 ft and the height (h) is 3 ft. So, let's calculate the diagonal:
d = √(5^2 + 3^2)
= √(25 + 9)
= √34 ft (approximately 5.83 ft)
Now, let's compare the diagonal of the window with the diameter of the table, which is twice the radius. The formula for the diameter (D) given the radius (r) is:
D = 2r
In this case, the radius (r) of the table is 4 ft. So, the diameter is:
D = 2 * 4 ft
= 8 ft
Since the diameter of the table (8 ft) is smaller than the diagonal of the window (approximately 5.83 ft), the table will indeed go through the window by leaning it over and moving it through the diagonal.