Question

the length of averys rectangular living room is 3 meters and the distance between opposite corners is 7 meters. what is the width of averys living room? if necessary, round to the nearest tenth. meters submit

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, the length \(l = 3\) meters, the diagonal \(d=7\) meters. Let the width be \(w\). By the Pythagorean theorem \(l^{2}+w^{2}=d^{2}\), so \(w^{2}=d^{2}-l^{2}\).

Step2: Substitute values

Substitute \(l = 3\) and \(d = 7\) into the formula: \(w^{2}=7^{2}-3^{2}=49 - 9=40\).

Step3: Solve for \(w\)

Take the square root of both sides: \(w=\sqrt{40}\approx6.3\) (rounded to the nearest tenth).

Answer:

\(6.3\)