Question

12. A long time ago Dulani found an island shaped like a triangle with three straight shores of length 3 km, 4 km and 5 km. He said nobody could come within 1 km of his shore. What was the area of his exclusion zone?​

Answer 1

Відповідь:

15.14 sq.km

Пояснення:

Dimensions 3km, 4km and 5km are pythagorean triplets, ie, the island is right triangle

shaped.

If you take 1km offshore the island, you will have three rectangles of dimensions

(5km,1km), (4km,1km), (3km,1km) and a complete circle of radius 1km.

Thus, the area of exclusion zone = sum of the areas of three rectangles + area of circle

= 5x1 + 4x1 + 3x1 + 3.14x1

= 15.14 sq.km

Answer 2

Dulani's island is shaped like a right-angled triangle with sides of lengths 3 km, 4 km, and 5 km. This is a Pythagorean triple, which means it satisfies the Pythagorean theorem (a^2 + b^2 = c^2) where 'a' and 'b' are the lengths of the shorter sides, and 'c' is the length of the hypotenuse (the longest side).

In this case, 'a' is 3 km, 'b' is 4 km, and 'c' is 5 km. So, we can use the Pythagorean theorem to find the length of the exclusion zone from Dulani's shore:

Exclusion Zone = c - 1 km Exclusion Zone = 5 km - 1 km Exclusion Zone = 4 km

Now, to find the area of his exclusion zone (assuming it's a circular exclusion zone around the island):

Area of Exclusion Zone = π * (Exclusion Zone)^2 Area of Exclusion Zone = π * (4 km)^2 Area of Exclusion Zone = π * 16 km^2 Area of Exclusion Zone ≈ 50.27 square kilometers

So, the area of Dulani's exclusion zone is approximately 50.27 square kilometers.