Question

caleb is replacing a door that measures 84 inches by 35 inches. what is the distance between opposite corners of the door? inches

Explanation:

Step1: Apply Pythagorean theorem

The door forms a rectangle. The distance between opposite corners (diagonal) \(d\) of a rectangle with length \(l = 84\) inches and width \(w=35\) inches can be found using the Pythagorean theorem \(d=\sqrt{l^{2}+w^{2}}\).
So, \(d = \sqrt{84^{2}+35^{2}}\).

Step2: Calculate \(l^{2}\) and \(w^{2}\)

\(84^{2}=84\times84 = 7056\), \(35^{2}=35\times35=1225\).
Then \(l^{2}+w^{2}=7056 + 1225=8281\).

Step3: Find the square - root

\(d=\sqrt{8281}\). Since \(91\times91 = 8281\), \(d = 91\).

Answer:

91