The side of a square is 10 meters longer than the side of an equilateral triangle. The perimeter of the sqaure is 3 times the perimeter of the triangle. Find the length of each side of the triangle.
represent unknowns using variables:
let x = length of a side of equilateral triangle
let x+10 = length of a side of square
*recall that perimeter of any polygon is the sum of the lengths of its sides,,
since square has 4 sides with equal lengths, and equilateral triangle has 3 sides with equal lengths:
P,square=4(x+10)
P,triangle=3x
thus:
4(x+10) = 3*(3x)
now simplify this, and solve for x.
Well, well, well, it seems we have a math problem in our hands. Let's put on our thinking caps and solve it!
Let's call the side length of the equilateral triangle "x." According to the problem, the side length of the square is 10 meters longer. So, the side length of the square is x + 10.
Now, the perimeter of an equilateral triangle can be found by simply multiplying the side length by 3. Therefore, the perimeter of the triangle is 3x.
The perimeter of a square is found by multiplying the side length by 4. So the perimeter of the square is 4(x + 10).
According to the problem, the perimeter of the square is three times the perimeter of the triangle. In other words, 4(x + 10) = 3(3x).
Now, all that's left is to solve for x. Let's distribute and simplify:
4x + 40 = 9x
Subtract 4x from both sides:
40 = 5x
Finally, divide both sides by 5:
x = 8
So the length of each side of the equilateral triangle is 8 meters. Ta-da! Puzzle solved.
Let's suppose the side length of the equilateral triangle is "x" meters.
According to the given information, the side of the square is 10 meters longer than the side of the equilateral triangle. Hence, the side length of the square is x + 10 meters.
The perimeter of the square is four times the side length. So, the perimeter of the square is 4(x + 10).
The perimeter of the equilateral triangle is three times the side length. Therefore, the perimeter of the equilateral triangle is 3x.
Given that the perimeter of the square is three times the perimeter of the equilateral triangle, we can set up the equation:
4(x + 10) = 3x
Expanding the equation:
4x + 40 = 3x
Subtracting 3x from both sides:
4x - 3x + 40 = 0
Simplifying the equation further gives:
x + 40 = 0
Subtracting 40 from both sides:
x = -40
Since the length of a side cannot be negative, we can conclude that there is no valid length for the side of the equilateral triangle in this scenario.
To solve this problem, we need to set up equations based on the given information.
Let's say that the side length of the equilateral triangle is "x" meters.
According to the problem, the side length of the square is 10 meters longer than the side length of the equilateral triangle, which means the side length of the square is "x + 10" meters.
Now, we know that the perimeter of a square is given by 4 times the side length, and the perimeter of an equilateral triangle is given by 3 times the side length.
Based on this information, we can set up the following equations:
Perimeter of square = 3 times perimeter of triangle
4*(x + 10) = 3*3*x
Simplifying the equation:
4x + 40 = 9x
Moving all the x terms to one side of the equation:
40 = 9x - 4x
40 = 5x
Now, we can solve for x by dividing both sides of the equation by 5:
x = 40/5
x = 8
Therefore, the length of each side of the equilateral triangle is 8 meters.