ABCD is a parallelogram. solve for x and find the lengths of BC=16+2x and AD=10+8x
BC = AD.
16 + 2X = 10 + 8X,
2X - 8X = 10 - 16,
-6X = -6,
X = -6 / -6 = 1.
BC = AD = 16 + 2X = 16 + 2 = 18.
Since ABCD is a parallelogram, opposite sides are congruent. Therefore, BC = AD.
Given:
BC = 16 + 2x
AD = 10 + 8x
Setting these expressions equal to each other:
16 + 2x = 10 + 8x
Now we can solve for x:
Move all terms with x to one side:
2x - 8x = 10 - 16
Combine like terms:
-6x = -6
Divide both sides by -6:
x = -6 / -6
Simplifying:
x = 1
Now that we have the value of x, we can substitute it back into the given expressions to find the lengths of BC and AD:
BC = 16 + 2(1) = 16 + 2 = 18
AD = 10 + 8(1) = 10 + 8 = 18
So, the lengths of BC and AD are both 18 units.
In order to solve for x and find the lengths of BC and AD, we can use the properties of parallelograms.
First, let's look at the given lengths of BC and AD:
BC = 16 + 2x
AD = 10 + 8x
Since ABCD is a parallelogram, opposite sides are equal. Therefore, we have:
BC = AD
Now, we can set up an equation by equating the given lengths:
16 + 2x = 10 + 8x
To solve for x, we will isolate the variable on one side of the equation. Let's begin:
Subtracting 2x from both sides:
16 = 10 + 6x
Next, subtracting 10 from both sides:
6 = 6x
Finally, dividing both sides by 6:
x = 1
So, x = 1.
Now that we have found the value of x, we can substitute it back into the expressions for BC and AD to find their lengths:
BC = 16 + 2x
BC = 16 + 2(1)
BC = 16 + 2
BC = 18
AD = 10 + 8x
AD = 10 + 8(1)
AD = 10 + 8
AD = 18
Therefore, the length of BC is 18 units and the length of AD is also 18 units.