Question

1. the length of a rectangle is 8 cm more than 3 times its width. the perimeter of the rectangle is 64 cm. show the equation that would be used to find the dimensions of the rectangle.

let ( w = ) the width. then ( 3w + 8 = ) length. so the equation is ( 64 = 2(3w + 8)+2w ).
let ( w = ) the width. then ( 3w = ) length + 8. so the equation is ( 64 = 2(3w - 8)+2w ).
let ( w = ) the width. then ( 3w + 8 = ) length. so the equation is ( 64 = 2(3(w + 8))+2w ).
let ( w = ) the width. then ( 3(w + 8)= ) length. so the equation is ( 64 = (3w + 8)w ).

Explanation:

Step1: Definir variables

Sea \( w \) el ancho del rectángulo.

Step2: Expresar la longitud

La longitud es \( 3w + 8 \) (8 cm más que 3 veces el ancho).

Step3: Usar la fórmula del perímetro

El perímetro \( P \) de un rectángulo es \( P=2(\text{longitud}+\text{ancho}) \). Dado que \( P = 64 \), entonces \( 64=2((3w + 8)+w) \). Simplificando: \( 64=2(3w + 8+w)=2(4w + 8)=8w+16 \).

Answer:

\( 64 = 2((3w + 8)+w) \)