In the accompanying diagram, the perimeter of isosceles triangle MNO is equal to the perimeter of square ABCD. If the sides of the triangle are represented by 4x+4 , 5x-3, 17 and one side of the square is represented by 3x, find the length of the square
To find the length of the square, we need to set up an equation using the given information.
The perimeter of the isosceles triangle MNO is given by the sum of its three sides:
Perimeter of MNO = 4x+4 + 5x-3 + 17
Similarly, the perimeter of the square ABCD can be found by adding up the lengths of all its sides:
Perimeter of ABCD = 4 * (length of one side)
Given that the length of one side of the square is represented by 3x, we can replace it in the equation:
Perimeter of ABCD = 4 * (3x)
Now we can set up an equation by equating the two perimeters:
4x+4 + 5x-3 + 17 = 4 * (3x)
Simplifying the equation:
9x + 18 = 12x
Moving all the terms containing x to one side:
12x - 9x = 18
3x = 18
Dividing both sides by 3:
x = 6
Now that we have found the value of x, we can substitute it back into the expression for one side of the square:
Length of one side of the square = 3x = 3 * 6 = 18
Therefore, the length of the square is 18 units.
To find the length of the square, we first need to set up an equation using the given information.
Let's denote the sides of the triangle as follows:
Side MN = 4x + 4
Side NO = 5x - 3
Side OM = 17
The perimeter of the triangle is given by the sum of its sides, so we can write:
Perimeter of triangle MNO = (4x + 4) + (5x - 3) + 17
The perimeter of the triangle is also equal to the perimeter of the square ABCD, which has side length represented by 3x. Therefore, we can write:
Perimeter of triangle MNO = Perimeter of square ABCD
(4x + 4) + (5x - 3) + 17 = 4 * (3x)
Now, solve this equation to find the value of x:
4x + 4 + 5x - 3 + 17 = 12x
9x + 18 = 12x
18 = 12x - 9x
18 = 3x
x = 6
Now that we have found the value of x, substitute it back into the expression for the side length of the square:
Side of square ABCD = 3x
Side of square ABCD = 3 * 6
Side of square ABCD = 18
Therefore, the length of square ABCD is 18.