Question

the length of karis rectangular living room is 3 meters and the distance between opposite corners is 8 meters. what is the width of karis living room? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Recall Pythagorean theorem

In a rectangle, the diagonal (distance between opposite corners) forms a right triangle with length and width. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the diagonal, \(a\) is length, \(b\) is width. Here, \(a = 3\), \(c=8\), find \(b\).

Step2: Rearrange formula for width

From \(a^{2}+b^{2}=c^{2}\), we get \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 3\), \(c = 8\): \(b=\sqrt{8^{2}-3^{2}}=\sqrt{64 - 9}=\sqrt{55}\).

Step3: Calculate and round

\(\sqrt{55}\approx7.4\) (rounded to nearest tenth).

Answer:

\(7.4\)