Respuesta :
Answer:
- The required dimensions of rectangle are 11 feet and 5 feet.
Step-by-step explanation:
Given, The length of a rectangle is 4 ft less than three times the width, and the area of the rectangle is 55 ft².
Let's assume width of rectangle be x feet and length be 3x - 4 feet. Using the formula of Area of rectangle we'll find the value of length and width.
[tex] \\ \dashrightarrow{ \red{ \underline{ \underline {\sf\: \:Area _{(rectangle)} = Length \times width}}}} \\ \\ [/tex]
Substituting the required values:
[tex]\dashrightarrow\: \: (3x - 4)(x) = 55 \\ [/tex]
[tex]\dashrightarrow\: \: 3x^2 - 4x = 55 \\ [/tex]
[tex]\dashrightarrow\: \: 3x^2 - 4x - 55 = 0 \\ [/tex]
[tex]\dashrightarrow\: \: 3x^2 + 11x - 15x - 55 = 0 \\ [/tex]
[tex]\dashrightarrow\: \: x(3x+11) -5(3x+11) = 0 \\ [/tex]
[tex]\dashrightarrow\: \: (x-5)(3x+11) = 0 \\ [/tex]
[tex] { \red{ \dashrightarrow\: \: { \underline{ \underline{ {x = 5 \: or \: \dfrac{-11}{3}}}}}}} \\ \\ [/tex]
Hence,
- Length of rectangle = 3x - 4 = 3(5) -4 = 11 feet
- Breadth of rectangle= x = 5 feet
[tex]\therefore[/tex] The required dimensions of rectangle are 11 feet and 5 feet.
