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QuestionFind xx if the length of DF‾\overline{D F} is (4x+2)(4x + 2) inches and DE‾\overline{D E} is 17 inches.

Studdy Solution

STEP 1

Assumptions1. The line segment F‾\overline{ F} has a length of (4x+)(4x +) inches. . Point is the midpoint of $\overline{ F}$.
3. The length of $\overline{}$ is17 inches.
4. Since is the midpoint of F‾\overline{ F}, the lengths of ‾\overline{} and F‾\overline{ F} are equal.

STEP 2

Since $$ is the midpoint of $\overline{ F}$, we can write the length of $\overline{ F}$ as twice the length of $\overline{}$.
F‾=2×‾\overline{ F} =2 \times \overline{}

STEP 3

Now, plug in the given values for the lengths of F‾\overline{ F} and ‾\overline{}.
(x+2)=2×17(x +2) =2 \times17

STEP 4

Calculate the right side of the equation.
(4x+2)=2×17=34(4x +2) =2 \times17 =34

STEP 5

Now, we have a simple linear equation to solve for xx.
4x+2=344x +2 =34

STEP 6

Subtract2 from both sides of the equation to isolate the term with xx.
4x=34−24x =34 -2

STEP 7

Calculate the right side of the equation.
4x=324x =32

STEP 8

Finally, divide both sides of the equation by4 to solve for xx.
x=32/4x =32 /4

STEP 9

Calculate the value of xx.
x=32/4=8x =32 /4 =8So, the value of xx is8.

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