Question

kaylas bedroom is rectangular. the length of one wall of kaylas bedroom is 2.8 meters. the length from one corner of the bedroom to the diagonally opposite corner is 4.7 meters. what is the length of the other wall? if necessary, round to the nearest tenth. meters submit

Explanation:

Step1: Identify the problem type

This is a right triangle problem where the diagonal is the hypotenuse (\(c = 4.7\) m) and one side is \(a = 2.8\) m. We use the Pythagorean theorem \(a^2 + b^2 = c^2\) to find the other side \(b\).

Step2: Rearrange the formula for \(b\)

From \(a^2 + b^2 = c^2\), we get \(b^2 = c^2 - a^2\), so \(b=\sqrt{c^2 - a^2}\).

Step3: Substitute the values

Substitute \(a = 2.8\) and \(c = 4.7\) into the formula:
\(b=\sqrt{4.7^2 - 2.8^2}\)
First, calculate \(4.7^2 = 22.09\) and \(2.8^2 = 7.84\).

Step4: Compute the difference

Subtract: \(22.09 - 7.84 = 14.25\).

Step5: Take the square root

\(b=\sqrt{14.25}\approx 3.8\) (rounded to the nearest tenth).

Answer:

3.8