Question

rico is planning to lay two decorative pieces of metal across the 45 - inch by 47 - inch rectangular glass centerpiece of a cabinet. each piece will lie on a diagonal of the centerpiece. each piece of metal should have a length of approximately _____ inches. round to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

Let the length and width of the rectangle be $a = 45$ inches and $b=47$ inches. The diagonal $d$ of a rectangle satisfies $d^{2}=a^{2}+b^{2}$. So $d=\sqrt{a^{2}+b^{2}}=\sqrt{45^{2}+47^{2}}$.

Step2: Calculate the squares

$45^{2}=45\times45 = 2025$ and $47^{2}=47\times47=2209$. Then $a^{2}+b^{2}=2025 + 2209=4234$.

Step3: Find the square - root

$d=\sqrt{4234}\approx65.07$ inches.

Answer:

$65.07$