Question

an architect is making a floor plan for a rectangular gymnasium. the distance between opposite corners of the gym will be 34 meters and the width will be 16 meters. what will be the length of the gym?
meters

Explanation:

Step1: Apply Pythagorean theorem

The distance between opposite corners of a rectangle is the diagonal, calculated by $d = \sqrt{l^2 + w^2}$, where $l=34$ m, $w=16$ m.

Step2: Calculate squared length/width

$34^2 = 1156$, $16^2 = 256$

Step3: Sum squared values

$1156 + 256 = 1412$

Step4: Compute square root

$\sqrt{1412} = \sqrt{4 \times 353} = 2\sqrt{353} \approx 37.58$

Answer:

$2\sqrt{353}$ (or approximately 37.58) meters