Final answer:
By applying the Pythagorean theorem to the right-angled triangle formed by the radius and the chord, we calculate the radius as 25 cm. Therefore, the diameter of the circle is twice the radius, which gives us 50 cm.
Step-by-step explanation:
To find the diameter of the circle when you have a chord that is 30 cm in length and a distance from the center to the chord (perpendicular from the center to the chord) of 20 cm, you can use the properties of a right triangle.
Imagine drawing a radius from the center of the circle to each end of the chord, forming a triangle with the chord as the base. Since the radii are equal in length, the chord bisects the triangle into two congruent right-angled triangles. The distance from the center to the chord is one of the heights of these triangles.
Using the Pythagorean theorem (a2 + b2 = c2), we can find the length of the radius (r). Let r represent the radius, and we have:
202 + (30/2)2 = r2
400 + 225 = r2
625 = r2
r = 25 cm
Once we have the radius, the diameter is simply twice the radius, which in this case is 25 cm × 2 = 50 cm. Therefore, the diameter of the circle is 50 cm.