Elliot is building a sandbox in the shape of a triangle. A model of the sandbox is shown. Which expression represents the perimeter of Elliot's sandbox?
bottom = x + 6
left side = /
the right side = x +4
x+11
3x−2
x+10
3x+10
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the bottom side has a length of x + 6, the left side has a length of x, and the right side has a length of x + 4.
Therefore, the expression that represents the perimeter of Elliot's sandbox is:
(x + 6) + x + (x + 4) = 3x + 10
To find the perimeter of Elliot's sandbox, we need to add up the lengths of all three sides of the triangle.
The bottom side has a length of x + 6.
The left side has a length of x.
The right side has a length of x + 4.
To find the perimeter, we add all three side lengths together:
Perimeter = (x + 6) + x + (x + 4)
Simplifying this expression, we get:
Perimeter = x + 6 + x + x + 4
Perimeter = 3x + 10
Therefore, the expression that represents the perimeter of Elliot's sandbox is 3x + 10.
To find the perimeter of Elliot's sandbox, we need to calculate the sum of the lengths of all the sides.
The bottom side has a length of x + 6.
The left side is not given, but it is shown as a diagonal symbol ("/"). This indicates that it is either an inclined line or a slanted side joining the bottom and the right side. Since the sandbox is in the shape of a triangle, we can assume it is a slanted side. To find the length of the left side, we can use the Pythagorean theorem.
Using the Pythagorean theorem, we can say that (the left side)^2 = (the bottom side)^2 + (the right side)^2. So ((left side)^2) = ((x + 6)^2 + (x + 4)^2).
Now, taking the square root of both sides, we will get the length of the left side as sqrt((x + 6)^2 + (x + 4)^2).
The right side has a length of x + 4.
To find the perimeter, we add up all the side lengths:
Perimeter = bottom + left side + right side
Perimeter = (x + 6) + sqrt((x + 6)^2 + (x + 4)^2) + (x + 4)
Simplifying this expression, we get:
Perimeter = 3x + sqrt((x + 6)^2 + (x + 4)^2) + 10
Therefore, the correct expression that represents the perimeter of Elliot's sandbox is: 3x + sqrt((x + 6)^2 + (x + 4)^2) + 10.