Question

pregunta 3 3 puntos
eloise was given the following problem: a rectangle has a width of 7.1 feet and a perimeter of 27.8 feet.

1. what is the length of the rectangle? l= ft
2. what is the area of the rectangle? a= ft²
3. to solve, eloise multiplied 7.1*27.8 and got 197.38 feet squared as her answer. her teacher told her this was incorrect. which best explains eloises error?

(type a, b, c, or d)
a. eloise didnt get the area formula right
b. eloise should have subtracted the two values instead of multiplying
c. eloises answer is too big
d. eloise used the perimeter as the length

Explanation:

Step1: Calcular la longitud

La fórmula del perímetro de un rectángulo es \( P = 2(l + w) \), donde \( P \) es el perímetro, \( l \) es la longitud y \( w \) es el ancho. Despejamos \( l \):
\( 27.8 = 2(l + 7.1) \)
Dividimos ambos lados por 2: \( 13.9 = l + 7.1 \)
Restamos 7.1: \( l = 13.9 - 7.1 = 6.8 \) ft.

Step2: Calcular el área

La fórmula del área de un rectángulo es \( A = l \times w \). Sustituimos \( l = 6.8 \) y \( w = 7.1 \):
\( A = 6.8 \times 7.1 = 48.28 \) \( \text{ft}^2 \).

Step3: Explicar el error de Eloise

Eloise multiplicó \( 7.1 \times 27.8 \), pero el área requiere la longitud (no el perímetro) multiplicada por el ancho. Entonces, usó el perímetro como longitud.

Answer:

1. \( l = 6.8 \) ft
2. \( A = 48.28 \) \( \text{ft}^2 \)
3. D