Question

1. the length of a rectangle is 5 centimeters less than twice its width. the perimeter of the rectangle is 80 cm. what are the dimensions of the rectangle?

length = 25 cm, width = 15 cm
length = 23 cm, width = 14 cm
length = 24 cm, width = 16 cm
length = 22 cm, width = 18 cm

Explanation:

Step1: Definir variables

Sea la anchura \( w \) y la longitud \( l = 2w - 5 \).

Step2: Usar la fórmula del perímetro

El perímetro \( P = 2(l + w) \). Sustituyendo \( l \) y \( P = 80 \):
\( 80=2((2w - 5)+w) \)

Step3: Simplificar la ecuación

\( 80 = 2(3w - 5) \)
\( 80 = 6w - 10 \)
\( 6w=80 + 10 \)
\( 6w = 90 \)
\( w=\frac{90}{6}=15 \)

Step4: Calcular la longitud

\( l = 2w - 5=2\times15 - 5=30 - 5 = 25 \)

Answer:

longitud = 25 cm, width = 15 cm