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The length of a rectangle is 10 ft less than three times the width, and the area of the rectangle is 77ft^2 . Find the dimensions of the rectangle.

Sagot :

Answer:

  • The dimensions of rectangle are 11 feet and 7 feet.

Step-by-step explanation:

Given, The length of a rectangle is 10 ft less than three times the width, and the area of the rectangle is 77 ft²

Let's assume width of rectangle be x feet and Length of rectangle be 3x - 10. Using the formula of area of the rectangle we'll find the dimensions of the Rectangle.

[tex] \\ \dashrightarrow{ \red{\underline{\underline{\sf{Area (rectangle) = Length \times width }}}}} \\ \\ [/tex]

Substituting the required values:

[tex]\dashrightarrow \: \: (3x-10)(x) = 77 \\ [/tex]

[tex]\dashrightarrow \: \: 3x^2 - 10x = 77 \\ [/tex]

[tex]\dashrightarrow \: \: 3x^2 -10x -77 = 0 \\ [/tex]

[tex]\dashrightarrow \: \:3x^2 + 11x -21x -77 = 0 \\ [/tex]

[tex]\dashrightarrow \: \: x(3x+11)-7(3x+11) = 0 \\ [/tex]

[tex]\dashrightarrow \: \: (x-7)(3x+11) = 0 \\ [/tex]

[tex]\dashrightarrow \: \: { \red{\underline{\underline { x = 7 \: or \: \dfrac{-11}{3}}}} } \\ \\ [/tex]

Hence,

  • Width of rectangle = x = 7 feet
  • Length of rectangle = 3x -10 = 3(7) - 10 = 11 feet

[tex] \therefore[/tex] The required dimensions of rectangle are 11 feet and 7 feet.

The dimensions of the given rectangle with an area of 77 ft^2 and given dimensions are; Length = 11 ft and Width = 7 ft

How to find the Area of a rectangle?

Formula for area of a rectangle is;

A = Length * Width

We are given;

Length; L = 3W - 10

Thus;

Area; A = W(3W - 10)

Thus;

W(3W - 10) = 77

3W² - 10W - 77 = 0

Using online quadratic equation calculator, we have;

W = 7

Thus;

L = (3*7) - 10

L = 11 ft

Read more about Rectangle Area at; https://brainly.com/question/13048427

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