The length of a rectangle is three times the length of a side of a square and the width of the rectangle is two less than the side of the square. If the perimeter of the rectangle is twenty eight more than the perimeter of the square, find the length of a side of the square. [ Only an algebraic solution will be accepted ]
If the width is x and the length is y, and the side of the square is s,
y = 3s
x = s-2
2(x+y) = 4s+24
s = ?
This taxi sign is 2.1 metres wide and 39cm tall. Assuming the ends are perfect semi-circles find the area in square metres to three significant figures.
To solve this problem, let's represent the unknown quantities:
Let's say the length of the rectangle is "L" and the width of the rectangle is "W".
The side of the square will be represented as "S".
From the given information, we can create equations:
1. The length of the rectangle is three times the length of a side of the square:
L = 3S
2. The width of the rectangle is two less than the side of the square:
W = S - 2
3. The perimeter of the rectangle is twenty-eight more than the perimeter of the square:
Perimeter of Rectangle = Perimeter of Square + 28
The perimeter of a rectangle is calculated by adding all its sides:
Perimeter of Rectangle = 2L + 2W
The perimeter of a square is calculated by multiplying the length of one side by 4:
Perimeter of Square = 4S
Now we can substitute these equations into the third equation:
2L + 2W = 4S + 28
Since L = 3S and W = S - 2, we can substitute these values:
2(3S) + 2(S - 2) = 4S + 28
Simplifying the equation:
6S + 2S - 4 = 4S + 28
Combine like terms:
8S - 4 = 4S + 28
Subtract 4S from both sides:
4S - 4 = 28
Add 4 to both sides:
4S = 32
Divide by 4:
S = 8
Therefore, the length of a side of the square is 8.