Question

brittany is replacing a door that measures 80 inches by 39 inches. what is the distance between opposite corners of the door?

inches

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Explanation:

Step1: Identify the problem type

The door is a rectangle, and the distance between opposite corners is the diagonal. We can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c = \sqrt{a^2 + b^2}\). Here, \(a = 80\) inches and \(b = 39\) inches.

Step2: Calculate \(a^2 + b^2\)

First, calculate \(80^2\) and \(39^2\). \(80^2=80\times80 = 6400\) and \(39^2 = 39\times39=1521\). Then, add them together: \(6400 + 1521=7921\).

Step3: Find the square root of the sum

Now, find the square root of 7921. Since \(89\times89 = 7921\), so \(\sqrt{7921}=89\).

Answer:

89