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Anastaziya [24]
2 years ago
14

The length of a rectangle is 4FT less than three times the width, and the area of the rectangle is 55FT. Find the dimensions of

the rectangle.
Mathematics
1 answer:
Umnica [9.8K]2 years ago
5 0

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.

\\ \dashrightarrow{ \red{ \underline{ \underline   {\sf\: \:Area  _{(rectangle)}  = Length \times width}}}} \\ \\

Substituting the required values:

\dashrightarrow\: \: (3x - 4)(x) = 55  \\

\dashrightarrow\: \: 3x^2 - 4x = 55 \\

\dashrightarrow\: \: 3x^2 - 4x - 55 = 0 \\

\dashrightarrow\: \: 3x^2 + 11x - 15x - 55 = 0 \\

\dashrightarrow\: \: x(3x+11) -5(3x+11) = 0 \\

\dashrightarrow\: \: (x-5)(3x+11) = 0 \\

{ \red{ \dashrightarrow\: \:   { \underline{ \underline{ {x = 5 \: or \: \dfrac{-11}{3}}}}}}} \\ \\

Hence,

  • Length of rectangle = 3x - 4 = 3(5) -4 = 11 feet
  • Breadth of rectangle= x = 5 feet

\therefore The required dimensions of rectangle are 11 feet and 5 feet.

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