Solution
Given:• The radius of the circle = 5
To find:• The perimeter of the shaded region
Approach and Working: Perimeter of the shaded region = length of arc CE + EF + BF +BC
• Length of arc EC = 2ᴨr/4 = 5ᴨ
• EF = AE – AF = 5 – AF
• FB = AD = 5
• BC = AC – AB = 5 – AB
Thus, the perimeter of the shaded region = 5ᴨ + (5 - AF) + 5 + (5 - AB) = 5ᴨ + 15 – (AB + AF)
Analysing Statement 1“The perimeter of the rectangle ABDF is 14”
• Implies, ABDF is a rectangle and 2(AB + AF) = 14
• Therefore, perimeter of the shaded region = 5ᴨ + 15 – (AB + AF) = 15 + 5ᴨ – 7 = 8 + 5ᴨ
Therefore, Statement 1 is sufficient to arrive at a unique answer
Analysing Statement 2“AB = 4/5 * AF”
• Perimeter of the shaded region = 5ᴨ + 15 – (AB + AF)
• However, we cannot find the value of AB or AF from the given information
Therefore, Statement 2 is NOT sufficient to arrive at a unique answer
Hence, the correct answer is option A.
Answer: AI think answer is D. because using AB=4/5 AF, we can substitue in AB^2+ AF^2 = 25 and get both AB and AF. and then find the perimeter.