Question

• cm = 2y + 38

follow these steps to find the lengths of bd and ac
steps

1. start with the equations for bm and dm.
2. abcd is a parallelogram. so, bm = dm. combine equations.
3. simplify and solve for x.
4. plug the value of x into the equation for bm.
5. multiply bm by 2 to find bd.
6. repeat steps 1 to 5 to find ac, by using the equations for am and cm and solving for y.

example
bm = 22 - 3x
dm = 10 + 9x
bm = dm
22 - 3x = 10 + 9x
12 = 12x
x = 1
bm = 22 - 3x
bm = 22 - 3(1)
bm = 19
2bm = bd
2( ) = bd
= bd

Explanation:

Step1: Set up the equation

Since in parallelogram \(ABCD\), \(BM = DM\), and \(BM=22 - 3x\), \(DM = 10+9x\), we have the equation \(22-3x=10 + 9x\).

Step2: Simplify the equation

Add \(3x\) to both sides: \(22=10 + 9x+3x\), which simplifies to \(22=10+12x\). Then subtract 10 from both sides: \(22 - 10=12x\), so \(12 = 12x\).

Step3: Solve for \(x\)

Divide both sides of \(12 = 12x\) by 12, we get \(x = 1\).

Step4: Find the length of \(BM\)

Substitute \(x = 1\) into the equation for \(BM\): \(BM=22-3(1)=19\).

Step5: Find the length of \(BD\)

Since \(BD = 2BM\), then \(BD=2\times19 = 38\).

Answer:

\(BD = 38\)