Question

se forma un jardín de rosas uniendo un rectángulo con un semicírculo, tal y como se muestra. el rectángulo mide 28 ft de largo y 17 ft de ancho. si el jardinero quiere cercar el jardín con valla, ¿cuántos pies de valla se requieren? (utilizar el valor 3.14 para π, y no redondear la respuesta. asegúrese de incluir las unidades correctas en la respuesta.)

Explanation:

Step1: Calculate perimeter of rectangle part

The rectangle has two lengths and one width involved in the fencing. The length is 28 ft and the width is 17 ft. The length - related part of the perimeter is \(2\times28\) ft and the width - related part is 17 ft. So the perimeter of the rectangle part is \(2\times28 + 17=56 + 17=73\) ft.

Step2: Calculate circumference of semi - circle

The diameter of the semi - circle is equal to the width of the rectangle, which is 17 ft. The formula for the circumference of a full circle is \(C = \pi d\), so the circumference of a semi - circle is \(C_{semicircle}=\frac{1}{2}\pi d\). Substituting \(d = 17\) ft and \(\pi=3.14\), we get \(C_{semicircle}=\frac{1}{2}\times3.14\times17 = 26.69\) ft.

Step3: Calculate total length of fencing

Add the perimeter of the rectangle part and the circumference of the semi - circle. The total length of fencing is \(73+26.69 = 99.69\) ft.

Answer:

99.69 ft