Question

lj is painting the rectangular ceiling in his living room. if the length of the ceiling is 18 feet and the width is 24 feet, what is the distance between opposite corners of the ceiling?

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, the length ($l = 18$), width ($w = 24$), and the diagonal ($d$) form a right - triangle. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where in a rectangle $l^{2}+w^{2}=d^{2}$.
So, $d^{2}=18^{2}+24^{2}$.

Step2: Calculate squares

$18^{2}=18\times18 = 324$ and $24^{2}=24\times24=576$. Then $d^{2}=324 + 576$.
$d^{2}=900$.

Step3: Find the square - root

Take the square - root of both sides to find $d$. Since $d>0$, $d=\sqrt{900}=30$.

Answer:

30 feet