Question

a rectangular window is 40 inches long with a diagonal of 58 inches. how wide is the window?

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the rectangle be $l = 40$ inches, the diagonal be $d=58$ inches, and the width be $w$. According to the Pythagorean theorem $l^{2}+w^{2}=d^{2}$. So $w^{2}=d^{2}-l^{2}$.

Step2: Substitute values

Substitute $l = 40$ and $d = 58$ into the equation: $w^{2}=58^{2}-40^{2}=(58 + 40)(58 - 40)$ (using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$). Then $w^{2}=(98)(18)=1764$.

Step3: Solve for $w$

Take the square root of both sides. Since $w>0$, $w=\sqrt{1764}=42$ inches.

Answer:

42 inches