Question

The following diagram shows a semicircle ABC with centre O and a right-angled triangle ACD.

Given the radius is 3.5 cm, calculate the perimeter, in cm, of the whole diagram.
A 36 B 60 C 67 D 72​

Answer 1

Since the radius is 3.5, to figure out the length on the diameter/side of the triangle, we have to multiply it by 2:

3.5 x 2 = 7

Now we can use the Pythagorean theorem to figure out the length of the other side of the triangle.

a^2 + b^2 = c^2

7^2 + b^2 = 25^2

49 + b^2 = 625

b^2 = 576

b = 24cm

Now that we have all the lengths of the triangle, using the radius, we can calculate the arc of the semi circle using the following formula:

(π + 2)r

(π + 2)3.5

3.5π + 7 = 18cm

Now we can add all of the lengths excluding the diameter of the circle since we want to calculate the perimeter:

25 + 24 + 18 = 67cm

Therefore, the correct answer would be C.