Mikhail used 220 inches of wire to make this figure.
this figure is made up two identical triangles,a 15 inch by 12 inch rectangle and a square of side 19 inches.Whatis the length of one side of each triangle if allthe sides of the triangles are equal in length.
I did this same problem 2 years ago
http://www.jiskha.com/display.cgi?id=1352760453
Looks like this teacher is just recycling the same problems
Let's start by calculating the total length of the wire used for the figure.
To find the length of one side of each triangle, we need to determine the perimeter of the triangles. The perimeter of each triangle can be calculated using the formula:
Perimeter = 3 * side length
Since the two triangles are identical, their perimeters will be the same. Let's denote the length of one side of each triangle as "x".
Now, let's calculate the perimeter of the two triangles:
Perimeter of triangles = 2 * (3 * x) = 6x
The figure also includes a rectangle and a square.
The perimeter of the rectangle can be calculated using the formula:
Perimeter of rectangle = 2 * (length + width) = 2 * (15 + 12) = 2 * 27 = 54 inches
The perimeter of the square can be calculated using the formula:
Perimeter of square = 4 * side length = 4 * 19 = 76 inches
The total perimeter of the figure is the sum of the perimeters of the triangles, the rectangle, and the square. It should be equal to the total wire used, which is 220 inches.
Total perimeter = Perimeter of triangles + Perimeter of rectangle + Perimeter of square
220 = 6x + 54 + 76
Now let's solve this equation for x:
220 = 6x + 54 + 76
220 - 54 - 76 = 6x
90 = 6x
x = 90/6
x = 15
Therefore, the length of one side of each triangle is 15 inches.
To find the length of one side of each triangle, we can start by determining the total length of wire used for the figure.
We know that Mikhail used 220 inches of wire. Let's add up the lengths of all the components:
- The two identical triangles have three sides each, so their total length is 6 times the length of one side.
- The rectangle has two sides of length 15 inches and two sides of length 12 inches, so its total length is 2 times the sum of those four sides.
- The square has four sides of equal length, so its total length is 4 times the length of one side.
Let x represent the length of one side of each triangle.
The total length of wire used can then be calculated as:
6x + 2(15 + 15 + 12 + 12) + 4(19) = 220.
Simplifying the equation, we have:
6x + 2(54) + 4(19) = 220.
6x + 108 + 76 = 220.
6x + 184 = 220.
6x = 36.
Dividing both sides by 6, we find:
x = 6.
Therefore, the length of one side of each triangle is 6 inches.