Question

1. a local businessman bought a square plot of land. the sides of the lot measure 32 feet on each side. he decides to split the lot into two equal - sized right triangles by putting a fence down the diagonal. approximately how many feet of fencing will he need?

Explanation:

Step1: Aplicar el Teorema de Pitágoras

El lado del cuadrado \(a = 32\) pies. La diagonal \(d\) de un cuadrado se calcula con la fórmula \(d=\sqrt{a^{2}+a^{2}}\) (Teorema de Pitágoras para un triángulo rectángulo con catetos \(a\) y \(a\)). Entonces \(d=\sqrt{32^{2}+32^{2}}\).

Step2: Simplificar la expresión

\(d=\sqrt{32^{2}(1 + 1)}=\sqrt{32^{2}\times2}\). Como \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 32^{2}\), \(b = 2\)), entonces \(d = 32\sqrt{2}\).

Step3: Calcular el valor numérico aproximado

Sabemos que \(\sqrt{2}\approx1.414\). Entonces \(d\approx32\times1.414 = 45.248\approx45.25\) pies.

Answer:

Aproximadamente \(45.25\) pies de valla.