Question

If 𝑪𝑫 = 𝟑cm, 𝑫𝑩 = 𝟒 cm, 𝑩𝑭 = 𝟒cm, 𝑭𝑬 = 𝟓 cm, 𝑨𝑩 = 𝟔 cm and ∠𝑪𝑨𝑫 ≅ ∠𝑫𝑨𝑩 ≅ ∠𝑩𝑨𝑭 ≅ ∠𝑭𝑨𝑬, then the perimeter of quadrilateral 𝑨𝑬𝑩𝑪 is ___.

• A. 28 cm
• B. 30 cm
• C. 26 cm
• D. 35 cm

Answer 1

The correct option is A 28 cm

AD is the angle bisector of angle 𝑪𝑨𝑩, so by the angle bisector theorem, 𝑪𝑫: 𝑩𝑫 = 𝑪𝑨: 𝑩𝑨.

$\frac{3}{4}=\frac{CA}{6}$

4$\times$CA = 18

CA = 4.5 cm

AF is the angle bisector of angle 𝑩𝑨𝑬, so by the angle bisector theorem, 𝑩𝑭:𝑬𝑭 = 𝑩𝑨:𝑬𝑨.

$\frac{4}{5}=\frac{6}{EA}$

4$\times$ EA = 30

EA = 7.5 cm

The perimeter of quadrilateral
𝑨𝑬𝑩𝑪 = 𝑪𝑫 + 𝑫𝑩 + 𝑩𝑭 + 𝑭𝑬 + 𝑬𝑨 + 𝑨𝑪
𝑨𝑬𝑩𝑪 = 𝟑 + 𝟒 + 𝟒 + 𝟓 + 𝟕. 𝟓 + 𝟒. 𝟓
𝑨𝑬𝑩𝑪 = 28 cm