The perimeter of the rectangle is
112 units. Find the length of side
PQ (bottom).
.
Write your answer without variables.
SR (top): 4z-2
SP (side):3z+2
The perimeter of the rectangle below is 174
units. Find the length of side WX
.
To find the length of side PQ (bottom) of the rectangle, we need to consider the formula for the perimeter of a rectangle.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P represents the perimeter, L represents the length, and W represents the width.
In this case, we are given the perimeter of the rectangle as 112 units. Therefore, we can substitute this value into the formula and solve for the length.
112 = 2L + 2W
Since the top and bottom sides of the rectangle are equal, we can substitute 4z-2 for both L and W.
112 = 2(4z-2) + 2(3z+2)
Simplifying the equation:
112 = 8z - 4 + 6z + 4
Combining like terms:
112 = 14z
To isolate z, we can divide both sides of the equation by 14:
112/14 = z
Simplifying:
8 = z
Therefore, the value of z is 8.
Now we can find the length of side PQ:
PQ = 4z - 2
Substituting z = 8:
PQ = 4(8) - 2
Simplifying:
PQ = 32 - 2
PQ = 30
So, the length of side PQ (bottom) is 30 units.
To find the length of side PQ (bottom) of the rectangle, we will use the formula for the perimeter of a rectangle, which is equal to the sum of all four sides.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Given the information:
SR (top) = 4z - 2
SP (side) = 3z + 2
We can let the length of the rectangle be SR and the width of the rectangle be SP. So, in this case, we have:
Length = SR = 4z - 2
Width = SP = 3z + 2
Now let's substitute these values into the perimeter formula:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (4z - 2 + 3z + 2)
Perimeter = 2 * (7z)
Perimeter = 14z
We also know from the given information that the perimeter of the rectangle is 112 units:
Perimeter = 14z = 112
Now we can solve this equation to find the value of z:
14z = 112
z = 112 / 14
z = 8
Finally, we can find the length of side PQ (bottom) by substituting the value of z back into the expression for the length of side PQ:
PQ = 3z + 2
PQ = 3(8) + 2
PQ = 24 + 2
PQ = 26
Therefore, the length of side PQ (bottom) is 26 units.
since the perimeter is the sum of the sides, the missing side x must be found using
(4z-2)+(3z+2)+x = 112
Now just solve that for x. Since you have not assigned a value to z, the answer for x will still involve z.