Question

Perimeter 84 Length 4 times it’s width What is area

Answer 1

Answer:

The solution is -

Step-by-step explanation:

To find the area

As two dimensions are given length and breadth so it means it is a rectangle

perimeter = 84 cm

Step = Let the width of the rectangle(2 dimensions) be 'x'[As per condition given in the question]

And,

Let the length of the rectangle be '4x'(4 times of x)[As per condition given in the question]

Perimeter of the rectangle given in the question = 84 cm(Given)

We know that perimeter = 2(a[Length] + b[Width or Breadth])

Equate the perimeter of the rectangle with its formula

That is,

84 = 2(a + b)

a = 4x(Length)

b = x(Width or Breadth)

84 = 2(4x + x)

Add the like terms

84 = 2(5x)

84 = 10x

Follow the rules of linear equation

x = 84/10

  = 42/5

  = 8.4 cm(Width or Breadth)

Length = 4x

            = 4(8.5)

            = 34 cm[or 34.0 cm]

We know that area of a rectangle = Length X Breadth(or Width)

Length = 34 cm

Width(or Breadth) = 8.4 cm

Area = 34 X 8.4

        = 285.6 $cm^{2}$

Answer 2

Step-by-step explanation:

Let the width of the rectangle =x

so, the length =4x

perimeter=84. (given)

perimeter of the rectangle=2(l+b)

84=2(4x+x)

84=2(5x)

84=10x

84/10=x

8.4=x

so,width of the rectangle=8.4unit

length of the rectangle=4×8.4=33.6

Area of the rectangle=l×b

=8.4×33.6

=282.24unit.