The perimeter of the figure is given by the sum of the lengths of the
external segments.
Response:
- The perimeter of the figure is approximately 117.1
Which methods can be used to find the perimeter of the figure?
The given parameters ate;
AC = 26
AD = BF
D = The midpoint of AC
Required:
The perimeter of the figure
Solution:
AD = CD = [tex]\dfrac{26}{2}[/tex] = 13
[tex]AE = \mathbf{\dfrac{AD}{sin(50^{\circ})} }= \dfrac{13}{sin(50^{\circ})} \approx17[/tex]
[tex]ED = \dfrac{AD}{tan(50^{\circ})} = \mathbf{\dfrac{13}{tan(50^{\circ})}} \approx 10.9[/tex]
AB = AC × tan(35°) = 26 × tan(35°) ≈ 18.2
[tex]\dfrac{18.2}{26} = \dfrac{13}{GF}[/tex], [tex]GF = 13 \times \dfrac{26}{18.2} \approx 18.6[/tex]
GF = HF = 18.6 by similar triangles
According to Pythagorean theorem, we have;
BH = √(18.6² + 13²) ≈ 22.7
BG = BH ≈ 22.7
BC = √(26² + 18.2²) ≈ 31.7
GC ≈ BC - BG, which gives;
GC = 31.7 - 22.7 ≈ 9
- The perimeter, P = AE + AB + BH + HF + GF + GC + CD
Which gives;
P ≈ 17 + 18.2 + 22.7 + 18.6 + 18.6 + 9 + 13 = 117.1
- The perimeter of the figure, P ≈ 117.1
Learn more about similar triangles here:
https://brainly.com/question/24031436
