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IN ∆ABC,D and E are the midpoints of AB and BC respectively. if DE = 2x +5 and AC is 5x + 6, find:
a. value of X
b. length of DE
c. length of AC

Sagot :

DubuChewyidn

IN ∆ABC,D and E are the midpoints of AB and BC respectively. if DE = 2x +5 and AC is 5x + 6, find:

  • a. value of X
  • b. length of DE
  • c. length of AC

Given:

  • AC = 5x + 6
  • DE = 2x + 5

In a triangle with midpoints D and E, we know that DE is parallel to AC and DE is half the length of AC.

[tex]\textsf{a. Value of x} : \\ \begin{align*} DE &= \frac{1}{2} AC \\ 2x + 5 &= \frac{1}{2} (5x + 6) \\ 2(2x + 5) = 5x + 6 \\ 4x + 10 &= 5x + 6 \\ 4x + 10 - 5x &= 6 \\ -x + 10 &= 6 \\ -x &= -4 \\ x &=4 \end{align*}[/tex][tex]\textsf{b. Length of } DE: \: \\ \begin{align*}DE &= 2x + 5 \\DE &= 2(4) + 5 \\DE &= 8 + 5 \\DE &= 13\end{align*}

[/tex][tex]\[ \boxed{\color{purple} \therefore \ \text{a. } \ x = 4 \quad \quad \quad \\ \text{b. Length of DE } = 13 \quad \quad \quad \\ \text{c. Length of AC } = 26} \] [/tex]