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QuestionFind the length of NO‾\overline{N O} given NP=3xN P=3x, NO=2xN O=2x, and OP=8O P=8.

Studdy Solution

STEP 1

Assumptions1. The line segment NP is divided into two segments NO and OP by point O. . The length of NP is given as3x.
3. The length of NO is given asx.
4. The length of OP is given as8.

STEP 2

Since point O is on the line segment NP, the sum of the lengths of NO and OP should be equal to the length of NP. We can express this relationship as an equation.
NP=NO+OPNP = NO + OP

STEP 3

Substitute the given lengths into the equation.
3x=2x+83x =2x +8

STEP 4

Rearrange the equation to isolate x on one side.
3x−2x=83x -2x =8

STEP 5

implify the left side of the equation to find the value of x.
x=8x =8

STEP 6

Now that we have the value of x, we can substitute it into the equation for NO to find the numerical length of NO.
NO=2xNO =2x

STEP 7

Substitute the value of x into the equation.
NO=2×NO =2 \times

STEP 8

Calculate the numerical length of NO.
NO=2×8=16NO =2 \times8 =16The numerical length of NO‾\overline{NO} is16.

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