Question

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

Explanation:

Step1: Identify the right - angled triangle

The door forms a rectangle. The distance between opposite corners is the length of the diagonal. The length and width of the door form the two legs of a right - angled triangle. Let $a = 80$ inches and $b = 39$ inches.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse (the diagonal of the rectangle). Substitute $a = 80$ and $b = 39$ into the formula: $c^{2}=80^{2}+39^{2}$. Calculate $80^{2}=6400$ and $39^{2}=1521$. Then $c^{2}=6400 + 1521=7921$.

Step3: Find the value of $c$

Take the square root of both sides to find $c$. Since $c=\sqrt{7921}$, and $\sqrt{7921}=89$.

Answer:

89