Find the values that make this a parallelogram?
The parallelogram is a square ans the values are:
on the outside of it is 17 y and 8y on the top and on the bottom it is 10 and 8x
On the inside of the square it is (3y-20) on the left hand corner and on the right hand it is (4y+4)
on the left hand bottom 4x+6 and right hand bottom (2x+6)
To determine the values that make this shape a parallelogram, we need to examine the properties of a parallelogram.
A parallelogram is a four-sided polygon in which opposite sides are parallel and congruent. Additionally, opposite angles are equal in a parallelogram.
Given that the shape in question is a square, we can deduce that all four sides are congruent and all four angles are right angles. So, we need to find the values for "x" and "y" that ensure the opposite sides are parallel and the opposite angles are equal.
Let's start by comparing the sides:
- The top and bottom sides have lengths of 8y and 10.
- The left and right sides have lengths of (3y - 20) and (4y + 4).
To make the opposite sides parallel:
- We need to equate the lengths of the top and bottom sides (8y = 10). Solving this equation, we find that y = 5/4.
Now let's focus on the angles:
- The opposite right angles (top right and bottom right) are already equal (90 degrees).
- The opposite left angles (top left and bottom left) need to be equal.
- (3y - 20) = (4y + 4). Solving this equation, we find that y = -24.
Now that we have found the values for y, we can substitute them back into the side lengths to ensure all four sides are congruent:
- The top and bottom sides: 8(5/4) = 10.
- The left and right sides: 3(-24) - 20 = 4(-24) + 4.
Thus, the values that make this shape a parallelogram (specifically, a square) are y = 5/4 and y = -24.