The length of a rectangle is three times the width if the length is increased by 4 cm and the width is decreased by 1 cm the perimeter will be 102 cm find the dimensions of the original rectangle

original Length = 36 cm

Original width = 12 cm

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The length of a rectangle is three times the width. It means that

L = 3W

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

if the length is increased by 4 cm and the width is decreased by 1 cm the perimeter will be 102 cm. This means that

2[(L + 4) + (W - 1)] = 102

Dividing through by 2, it becomes

L + 4 + W - 1 = 51

L + W + 4 - 1 = 51

L + W + 3 = 51

L + W = 51 - 3

L + W = 48 - - - - - - - - - - - -1

Substituting L = 3W into equation 1, it becomes

3W + W = 48

4W = 48

W = 48/4

W = 12

L = 3W = 3 × 12

L = 36

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions