Question

a windowpane is 7.4 inches by 6.4 inches. what is the distance between opposite comers of the windowpane? if necessary, round to the nearest tenth. inches submit

Explanation:

Step1: Apply Pythagorean theorem

The windowpane is a rectangle. Let \(a = 7.4\) and \(b=6.4\). The distance \(d\) between opposite corners (diagonal) of a rectangle is given by \(d=\sqrt{a^{2}+b^{2}}\) (from the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse of a right - triangle formed by the sides of the rectangle).
Substitute \(a = 7.4\) and \(b = 6.4\) into the formula: \(d=\sqrt{(7.4)^{2}+(6.4)^{2}}\).
First, calculate \((7.4)^{2}=7.4\times7.4 = 54.76\) and \((6.4)^{2}=6.4\times6.4=40.96\).
Then \(a^{2}+b^{2}=54.76 + 40.96=95.72\).
So \(d=\sqrt{95.72}\).

Step2: Calculate the square root

Using a calculator, \(\sqrt{95.72}\approx9.8\) (rounded to the nearest tenth).

Answer:

\(9.8\)