Question

the length of bonnies rectangular living room is 5 meters and the distance between opposite corners is 7 meters. what is the width of bonnies living room? if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the width be \(w\). In a rectangle, \(l^{2}+w^{2}=d^{2}\), where \(l = 5\) (length), \(d = 7\) (diagonal). So \(5^{2}+w^{2}=7^{2}\).

Step2: Simplify the equation

\(25+w^{2}=49\). Then \(w^{2}=49 - 25\).

Step3: Calculate \(w^{2}\)

\(w^{2}=24\).

Step4: Solve for \(w\)

\(w=\sqrt{24}\approx4.9\) (rounded to the nearest tenth).

Answer:

\(4.9\)