Question

Q1. The length of a rectangle is 6cm less than three times its width. The perimeter of the rectangle is 140 cm. Find the dimensions of the rectangle. By using Matrix Inversion Method and Cramer’s Rule.

Answer 1

The length of the rectangle is 51 cm.

The breadth of the rectangle is 19 cm.

Given: The length of a rectangle is 6 cm less than three times its width. The perimeter of the rectangle is 140 cm.

To Find: The dimensions of the rectangle.

Solution:

The perimeter of a rectangle can be given by the formula,

            Perimeter = 2 × ( L + B )                                          .....(1)

Where L = the length, B = the breadth.

Coming to the numerical,

Let the width of the rectangle be 'x'.

So, the length of the rectangle is = 3x - 6

The perimeter of the rectangle is = 140 cm

Putting respective values in (1), we get;

             Perimeter = 2 × ( L + B )  

         ⇒  140 = 2 × ( 3x - 6 + x )

         ⇒  4x - 6 = 70

         ⇒  4x = 76

         ⇒   x = 76/4

                  = 19 cm

The width of the rectangle is = 19 cm

The length of the rectangle is = 3x - 6 = ( 3× 19 ) - 6

                                                  = 51 cm

Hence,

The length of the rectangle is 51 cm.

The breadth of the rectangle is 19 cm.

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Answer 2

Answer:

length = 51 cm

breadth = 19 cm

Step-by-step explanation:

Given:

Perimeter = 140 cm

Rectangle length = 6 cm

To find:

Dimension

Solution:

The perimeter of a two-dimensional shape is the boundary or path that surrounds it, to put it simply. Although the perimeter of the rectangle will receive greater attention in this article, you may also calculate the perimeter for other forms.

A rectangle can be described as a quadrilateral with four sides in Euclidean plane geometry. Rectangulus, a combination of the Latin words angulus (angle) and rectus, is whence the English word "rectangle" originates (proper and right).

A rectangular form always has the same or identical sides on either side.

Rectangles have angles that measure 90 degrees apiece, if you measure the angles of a rectangle.

The following formula can be used to determine a rectangle's perimeter:

$Perimeter=2\times(L+B)$

Let us consider the breadth of the rectangle to be x and the length be 3x-6

Substituting the value of perimeter in equation,

$140=2\times(3x-6+x)\\140=2\times(4x-6)\\\frac{140}{2} =4x-6\\70=4x-6\\4x=76\\x=\frac{76}{4}\\ x=19cm$

Thus breadth x= 19cm

So length = 3x-16=51cm

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