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Question
The points
N,O,P and
Q all lie on the same line segment, in that order, such that the ratio of
NO:OP:PQ is equal to
3:3:2. If
NQ=8, find
PQ.
Answer Attempt 1 out of 2

PQ=

Question $\newline$ The points $\mathrm{N}, \mathrm{O}, \mathrm{P}$ and $\mathrm{Q}$ all lie on the same line segment, in that order, such that the ratio of $N O: O P: P Q$ is equal to $3: 3: 2$ . If $N Q=8$ , find $P Q$ . $\newline$ Answer Attempt $1$ out of $2$ $\newline$ $P Q=$

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Write equations of sine and cosine functions using properties

Full solution

Q. Question

\newline

The points

\mathrm{N}, \mathrm{O}, \mathrm{P}

and

\mathrm{Q}

all lie on the same line segment, in that order, such that the ratio of

N O: O P: P Q

is equal to

3: 3: 2

. If

N Q=8

, find

P Q

.

\newline

Answer Attempt

1

out of

2

\newline

P Q=

Assign Variables: Since the ratio of $NO:OP:PQ$ is $3:3:2$ , let's assign variables to each segment: let $NO = 3x$ , $OP = 3x$ , and $PQ = 2x$ .
Calculate Total Length: The total length $NQ$ is the sum of $NO$ , $OP$ , and $PQ$ , which is $3x + 3x + 2x = 8x$ .
Set Up Equation: We know $NQ = 8$ , so we can set up the equation $8x = 8$ .
Solve for x: Solving for x gives us $x = \frac{8}{8} = 1$ .
Find PQ: Now we can find PQ by multiplying the value of $x$ by the ratio for PQ: $PQ = 2x = 2 \times 1 = 2$ .

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