Question

a door is 7 feet 9 inches tall and 48 inches wide. can an 8 - foot - square piece of plywood be carried through the door? can an 8 - foot - square piece of plywood be carried through the door? no yes

Explanation:

Step1: Convert units

First, convert the height of the door to inches. Since 1 foot = 12 inches, 7 feet 9 inches = \(7\times12 + 9=93\) inches. The width of the door is 48 inches.

Step2: Calculate the diagonal of the door

Use the Pythagorean theorem \(d=\sqrt{h^{2}+w^{2}}\), where \(h = 93\) inches and \(w = 48\) inches. So \(d=\sqrt{93^{2}+48^{2}}=\sqrt{8649 + 2304}=\sqrt{10953}\approx104.66\) inches.

Step3: Convert the side - length of the plywood to inches

The side - length of the 8 - foot square plywood is \(8\times12 = 96\) inches. The diagonal of the square plywood is \(s\sqrt{2}\) (where \(s = 96\) inches), so \(d_{plywood}=96\sqrt{2}\approx96\times1.414 = 135.74\) inches. But we can also just compare the side - length of the plywood (96 inches) with the diagonal of the door (104.66 inches).

Answer:

Yes