Math / Geometry

QuestionFind the value of $c$ and $Y Z$ if $Y$ is between $X$ and $Z$ . $\begin{array}{l} X Y=11, Y Z=4 c, X Z=83 \\ c= \end{array}$ $\square$ $Y Z=$ $\square$

Studdy Solution

STEP 1

1. Point $Y$ is between points $X$ and $Z$ on a line segment.
2. The length of $XY$ is $11$ .
3. The length of $YZ$ is $4c$ .
4. The total length of $XZ$ is $83$ .

STEP 2

1. Set up the equation for the total length of the segment $XZ$ .
2. Solve for $c$ .
3. Calculate $YZ$ .

STEP 3

Set up the equation for the total length of the segment $XZ$ :
Since $Y$ is between $X$ and $Z$ , we have:
$XY + YZ = XZ$
Substitute the given values:
$11 + 4c = 83$

STEP 4

Solve for $c$ :
Subtract $11$ from both sides of the equation:
$4c = 83 - 11$
$4c = 72$
Divide both sides by $4$ :
$c = \frac{72}{4}$
$c = 18$

STEP 5

Calculate $YZ$ :
Substitute the value of $c$ into the expression for $YZ$ :
$YZ = 4c$
$YZ = 4 \times 18$
$YZ = 72$
The value of $c$ is:
$\boxed{18}$
The length of $YZ$ is:
$\boxed{72}$

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QuestionFind the value of $c$ and $Y Z$ if $Y$ is between $X$ and $Z$ . $\begin{array}{l} X Y=11, Y Z=4 c, X Z=83 \\ c= \end{array}$ $\square$ $Y Z=$ $\square$

Studdy Solution

STEP 1

1. Point $Y$ is between points $X$ and $Z$ on a line segment.
2. The length of $XY$ is $11$ .
3. The length of $YZ$ is $4c$ .
4. The total length of $XZ$ is $83$ .

STEP 2

1. Set up the equation for the total length of the segment $XZ$ .
2. Solve for $c$ .
3. Calculate $YZ$ .

STEP 3

Set up the equation for the total length of the segment $XZ$ :
Since $Y$ is between $X$ and $Z$ , we have:
$XY + YZ = XZ$
Substitute the given values:
$11 + 4c = 83$

STEP 4

Solve for $c$ :
Subtract $11$ from both sides of the equation:
$4c = 83 - 11$
$4c = 72$
Divide both sides by $4$ :
$c = \frac{72}{4}$
$c = 18$

STEP 5

Calculate $YZ$ :
Substitute the value of $c$ into the expression for $YZ$ :
$YZ = 4c$
$YZ = 4 \times 18$
$YZ = 72$
The value of $c$ is:
$\boxed{18}$
The length of $YZ$ is:
$\boxed{72}$

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QuestionFind the value of ccc and YZY ZYZ if YYY is between XXX and ZZZ. XY=11,YZ=4c,XZ=83c=\begin{array}{l} X Y=11, Y Z=4 c, X Z=83 \\ c= \end{array}XY=11,YZ=4c,XZ=83c=​ □\square□ YZ=Y Z=YZ= □\square□

Studdy Solution

STEP 1

1. Point Y Y Y is between points X X X and Z Z Z on a line segment.2. The length of XY XY XY is 11 11 11.3. The length of YZ YZ YZ is 4c 4c 4c.4. The total length of XZ XZ XZ is 83 83 83.

STEP 2

1. Set up the equation for the total length of the segment XZ XZ XZ.2. Solve for c c c.3. Calculate YZ YZ YZ.

STEP 3

Set up the equation for the total length of the segment XZ XZ XZ:Since Y Y Y is between X X X and Z Z Z, we have:XY+YZ=XZ XY + YZ = XZ XY+YZ=XZSubstitute the given values:11+4c=83 11 + 4c = 83 11+4c=83

STEP 4

Solve for c c c:Subtract 11 11 11 from both sides of the equation:4c=83−11 4c = 83 - 11 4c=83−114c=72 4c = 72 4c=72Divide both sides by 4 4 4:c=724 c = \frac{72}{4} c=472​c=18 c = 18 c=18

STEP 5

Calculate YZ YZ YZ:Substitute the value of c c c into the expression for YZ YZ YZ:YZ=4c YZ = 4c YZ=4cYZ=4×18 YZ = 4 \times 18 YZ=4×18YZ=72 YZ = 72 YZ=72 The value of c c c is:18 \boxed{18} 18​The length of YZ YZ YZ is:72 \boxed{72} 72​

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QuestionFind the value of $c$ and $Y Z$ if $Y$ is between $X$ and $Z$ . $\begin{array}{l} X Y=11, Y Z=4 c, X Z=83 \\ c= \end{array}$ $\square$ $Y Z=$ $\square$

1. Point $Y$ is between points $X$ and $Z$ on a line segment.
2. The length of $XY$ is $11$ .
3. The length of $YZ$ is $4c$ .
4. The total length of $XZ$ is $83$ .

1. Set up the equation for the total length of the segment $XZ$ .
2. Solve for $c$ .
3. Calculate $YZ$ .

Set up the equation for the total length of the segment $XZ$ :
Since $Y$ is between $X$ and $Z$ , we have:
$XY + YZ = XZ$
Substitute the given values:
$11 + 4c = 83$

Solve for $c$ :
Subtract $11$ from both sides of the equation:
$4c = 83 - 11$
$4c = 72$
Divide both sides by $4$ :
$c = \frac{72}{4}$
$c = 18$

Calculate $YZ$ :
Substitute the value of $c$ into the expression for $YZ$ :
$YZ = 4c$
$YZ = 4 \times 18$
$YZ = 72$
The value of $c$ is:
$\boxed{18}$
The length of $YZ$ is:
$\boxed{72}$