The perimeter of the rectangle below is 150 units. Find the length of side PQ and write the answer with no variables.
side 4x+3
Bottom: 5x
I meant top 5x oops
So the top is different from the bottom? Strange rectangle :(
In my sketch
4x+3 + 4x+3 + 5x + 5x = 150
18 x + 6 = 150
18 x = 144
etc etc etc
To find the length of side PQ, we need to use the formula for the perimeter of a rectangle, which is 2(length + width).
Given that the perimeter is 150 units, we can set up the equation as follows:
2(4x+3 + 5x) = 150
Simplifying the equation, we have:
2(9x + 3) = 150
Expanding the brackets, we have:
18x + 6 = 150
Next, we can isolate the x term by subtracting 6 from both sides:
18x = 144
Now, we can divide both sides by 18 to solve for x:
x = 144/18
Simplifying, we have:
x = 8
Now that we have the value of x, we can substitute it back into the given expressions to find the length of side PQ:
Length of PQ = 4x + 3
= 4(8) + 3
= 32 + 3
= 35
Therefore, the length of side PQ is 35 units.
To find the length of side PQ, we need to use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, the bottom side of the rectangle is given as 5x, and the side opposite to the bottom side (PQ) is given as 4x + 3. We are told that the perimeter is 150 units. So, we can write the equation as:
150 = 2(5x) + 2(4x + 3)
Simplifying this equation:
150 = 10x + 8x + 6
Combining like terms:
150 = 18x + 6
We want to find the value of x, and then substitute it into 4x + 3 to get the length of side PQ.
Subtracting 6 from both sides:
144 = 18x
Dividing both sides by 18:
8 = x
Now that we have the value of x, we can substitute it into 4x + 3 to find the length of side PQ:
PQ = 4(8) + 3 = 32 + 3 = 35
Therefore, the length of side PQ is 35 units.