Math / Geometry

QuestionIn parallelogram $LMNP$ if $LQ = 13$ find $LN$ .

Studdy Solution

STEP 1

What is this asking? If $LQ = 13$ , how long is $LN$ in parallelogram $LMNP$ ? Watch out! Don't forget that diagonals of a parallelogram bisect each other!

STEP 2

1. Use Parallelogram Properties
2. Calculate LN

STEP 3

The diagonals of a parallelogram bisect each other.
This means they cut each other perfectly in half!
In our case, the diagonals $LN$ and $MP$ intersect at point $Q$ .
So, $Q$ is the midpoint of both diagonals.

STEP 4

Since $Q$ is the midpoint of $LN$ , we know that $LQ$ is half the length of $LN$ .
We can write this mathematically as: $LQ = \frac{1}{2} \cdot LN$

STEP 5

We're given that $LQ = 13$ .
Let's plug this value into our equation: $13 = \frac{1}{2} \cdot LN$

STEP 6

To solve for $LN$ , we need to get it by itself.
We can do this by multiplying both sides of the equation by $2$ : $2 \cdot 13 = 2 \cdot \frac{1}{2} \cdot LN$ $26 = 1 \cdot LN$

STEP 7

So, we have: $LN = 26$

STEP 8

The length of $LN$ is $\textbf{26}$ .

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QuestionIn parallelogram $LMNP$ if $LQ = 13$ find $LN$ .

Studdy Solution

STEP 1

What is this asking? If $LQ = 13$ , how long is $LN$ in parallelogram $LMNP$ ? Watch out! Don't forget that diagonals of a parallelogram bisect each other!

STEP 2

1. Use Parallelogram Properties
2. Calculate LN

STEP 3

The diagonals of a parallelogram bisect each other.
This means they cut each other perfectly in half!
In our case, the diagonals $LN$ and $MP$ intersect at point $Q$ .
So, $Q$ is the midpoint of both diagonals.

STEP 4

Since $Q$ is the midpoint of $LN$ , we know that $LQ$ is half the length of $LN$ .
We can write this mathematically as: $LQ = \frac{1}{2} \cdot LN$

STEP 5

We're given that $LQ = 13$ .
Let's plug this value into our equation: $13 = \frac{1}{2} \cdot LN$

STEP 6

To solve for $LN$ , we need to get it by itself.
We can do this by multiplying both sides of the equation by $2$ : $2 \cdot 13 = 2 \cdot \frac{1}{2} \cdot LN$ $26 = 1 \cdot LN$

STEP 7

So, we have: $LN = 26$

STEP 8

The length of $LN$ is $\textbf{26}$ .

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QuestionIn parallelogram LMNPLMNPLMNP if LQ=13LQ = 13LQ=13 find LNLNLN.

Studdy Solution

STEP 1

What is this asking? If LQ=13LQ = 13LQ=13, how long is LNLNLN in parallelogram LMNPLMNPLMNP? Watch out! Don't forget that diagonals of a parallelogram bisect each other!

STEP 2

1. Use Parallelogram Properties2. Calculate LN

STEP 3

The diagonals of a parallelogram *bisect* each other.This means they cut each other perfectly in half!In our case, the diagonals LNLNLN and MPMPMP intersect at point QQQ.So, QQQ is the **midpoint** of *both* diagonals.

STEP 4

Since QQQ is the midpoint of LNLNLN, we know that LQLQLQ is **half** the length of LNLNLN.We can write this mathematically as: LQ=12⋅LNLQ = \frac{1}{2} \cdot LNLQ=21​⋅LN

STEP 5

We're given that LQ=13LQ = 13LQ=13.Let's **plug this value** into our equation: 13=12⋅LN13 = \frac{1}{2} \cdot LN13=21​⋅LN

STEP 6

To **solve for** LNLNLN, we need to get it by itself.We can do this by multiplying both sides of the equation by 222: 2⋅13=2⋅12⋅LN2 \cdot 13 = 2 \cdot \frac{1}{2} \cdot LN2⋅13=2⋅21​⋅LN 26=1⋅LN26 = 1 \cdot LN26=1⋅LN

STEP 7

So, we have: LN=26LN = 26LN=26

STEP 8

The length of LNLNLN is 26\textbf{26}26.

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QuestionIn parallelogram $LMNP$ if $LQ = 13$ find $LN$ .

What is this asking? If $LQ = 13$ , how long is $LN$ in parallelogram $LMNP$ ? Watch out! Don't forget that diagonals of a parallelogram bisect each other!

1. Use Parallelogram Properties
2. Calculate LN

The diagonals of a parallelogram bisect each other.
This means they cut each other perfectly in half!
In our case, the diagonals $LN$ and $MP$ intersect at point $Q$ .
So, $Q$ is the midpoint of both diagonals.

Since $Q$ is the midpoint of $LN$ , we know that $LQ$ is half the length of $LN$ .
We can write this mathematically as: $LQ = \frac{1}{2} \cdot LN$

We're given that $LQ = 13$ .
Let's plug this value into our equation: $13 = \frac{1}{2} \cdot LN$

To solve for $LN$ , we need to get it by itself.
We can do this by multiplying both sides of the equation by $2$ : $2 \cdot 13 = 2 \cdot \frac{1}{2} \cdot LN$ $26 = 1 \cdot LN$

So, we have: $LN = 26$

The length of $LN$ is $\textbf{26}$ .