Answered

IDNStudy.com, ang iyong gabay para sa maaasahan at mabilis na mga sagot. Ang aming platform ay nagbibigay ng mga maaasahang sagot upang matulungan kang gumawa ng matalinong desisyon nang mabilis at madali.

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]

Salamat sa iyong pakikilahok. Huwag kalimutang magtanong at magbahagi ng iyong kaalaman. Ang iyong ambag ay napakahalaga sa aming komunidad. Umaasa kami na natagpuan mo ang hinahanap mo sa IDNStudy.com. Bumalik ka para sa mas maraming solusyon!