contestada

A rectangle has a width of 6 inches. The area of the rectangle is 2 inches less than the perimeter. What is the length of the rectangle?

Respuesta :

adioabiola

The length of the rectangle in discuss is; 2.5 inches

Perimeter and area of a rectangle

The area of the rectangle is 2 inches less than the perimeter.

  • A = 2l +2w -2

The perimeter, p = 2l + 2(6)

  • A = 2l +12 -2

  • A = 2l +10

  • Area, A = lw

  • A = 6l

Therefore;

  • 6l = 2l +10

  • 4l = 10

l = 2.5 inches.

Read more on perimeter of a rectangle;

https://brainly.com/question/24571594

Lanuel

Based on the calculations, the length of the rectangle is equal to 2.5 inches.

  • Let the length of the rectangle be L.
  • Let the width of the rectangle be W.
  • Let the perimeter of the rectangle be P.
  • Let the area of the rectangle be P.

Given the following data:

  • Width = 6 inches

Translating the word problem into an algebraic equation, we have;

The area of the rectangle is 2 inches less than the perimeter:

[tex]A=P-2[/tex]  ....equation 1

The formula for perimeter of a rectangle.

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]P=2(L+W)[/tex]   ....equation 2

Substituting eqn. 2 into eqn. 1, we have:

[tex]A=2(L+W) -2\\\\A=2L+2(6)-2\\\\A=2L+10[/tex]...equation 3.

Also, the area of the rectangle is given by:

[tex]A=LW\\\\A=6L[/tex]...equation 4.

Equating eqn. 3 and eqn. 4, we have:

[tex]6L=2L+10\\\\6L-2L=10\\\\4L=10\\\\L=\frac{10}{4}[/tex]

Length = 2.5 inches.

Read more on perimeter of a rectangle here: https://brainly.com/question/17297081

Otras preguntas