The width of a rectangle is three fourths of the length. The perimeter of the rectangle becomes 50 cm when the legth and the width are each increased by two cm. Find the length and the width

Looks like a case for substitution.

width = w
length = l

width = 3/4 length
w = 3/4l

2(w + 2) + 2(l + 2) = 50cm
(2w + 4) + (2l + 4) = 50cm

Substitute w with the information you were given earlier (the width of a rectangle is three fourths the length):

2(3/4l) + 4 + 2l + 4 = 50cm
2(3/4l) + 2l + 8 = 50cm
6/4l + 2l = 42cm
1.5l + 2l = 42cm
3.5l = 42cm
l = 12cm

3/4(12cm) = 9cm

length = 12cm
width = 9cm

what is the perimeter of the rectangle w/ length x+4/x+3 and width 2x-3/x+3

Let's assume the length of the rectangle is "L" cm.

Given that the width of the rectangle is three-fourths of the length, we can express the width as (3/4)L cm.

The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)

In this case, when the length and width are each increased by two cm, the new length would be (L + 2) cm, and the new width would be ((3/4)L + 2) cm.

Given that the new perimeter is 50 cm, we can set up the equation:

50 = 2((L + 2) + ((3/4)L + 2))

Simplifying the equation, we get:

50 = 2(L + (3/4)L + 4)

50 = 2(7/4L + 4)

Now, let's solve for L:

50 = (7/2)L + 8

42 = (7/2)L

Multiplying both sides by 2/7 to isolate L:

L = (2/7) * 42

L = 12 cm

Now, substitute the value of L back into the expression for the width:

Width = (3/4)L = (3/4) * 12 cm = 9 cm

Therefore, the length of the rectangle is 12 cm, and the width is 9 cm.

To find the length and width of the rectangle, we can set up a system of equations based on the information given.

Let's start by defining our variables:
Let L = length of the rectangle
Let W = width of the rectangle

We are given two pieces of information:

1. The width is three-fourths of the length: W = (3/4)L.

2. When both the length and width are increased by 2 cm, the perimeter of the rectangle becomes 50 cm.

The perimeter of a rectangle is given by the formula: P = 2L + 2W.

Using the second piece of information, we can create the equation:
50 = 2(L + 2) + 2(W + 2)

Simplifying this equation, we get:
50 = 2L + 4 + 2W + 4
50 = 2L + 2W + 8

Now we can substitute the value of W from the first equation into the second equation:
50 = 2L + 2((3/4)L) + 8

Simplifying further, we have:
50 = 2L + (3/2)L + 8
50 = (7/2)L + 8

To isolate L, subtract 8 from both sides:
42 = (7/2)L

Now multiply both sides by (2/7):
(2/7) * 42 = L
12 = L

Therefore, the length of the rectangle is 12 cm.

To find the width, substitute the value of L into the first equation:
W = (3/4)L
W = (3/4) * 12
W = 9 cm

So, the length of the rectangle is 12 cm and the width is 9 cm.