Question

reagan measured the floor of her storage unit, which is rectangular. it is 8.3 meters wide and 9.5 meters from one corner to the opposite corner. how long is the storage unit? if necessary, round to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the length be $l$, width $w = 8.3$ meters and diagonal $d=9.5$ meters. According to the Pythagorean theorem $l^{2}+w^{2}=d^{2}$, so $l=\sqrt{d^{2}-w^{2}}$.

Step2: Substitute values

Substitute $d = 9.5$ and $w = 8.3$ into the formula: $l=\sqrt{9.5^{2}-8.3^{2}}=\sqrt{(9.5 + 8.3)(9.5 - 8.3)}=\sqrt{17.8\times1.2}=\sqrt{21.36}$.

Step3: Calculate the square - root

$\sqrt{21.36}\approx4.6$ (rounded to the nearest tenth).

Answer:

$4.6$