If the area of a circle is equal to the sum of the areas of two circles of diameters 10cm and 24cm, then the diameter of the larger circle (in cm) is:

Radius of the first circle r1 = 10/2 = 5cm.
Radius of the second circle r2 = 24/2 = 12cm.
∴Sum of their area = πr1² + πr2² = π5² + π12² = 25π + 144π = 169π.
Let the radius of the larger circle be r.
∴Area = πr².
According to the question:
⇒ πr² = 169π
⇒ r² = 169
⇒ r = √169 = 13cm
∴Radius of the large circle = 13cm.
Then, diameter of the larger circle = 13 × 2 = 26cm.
Therefore, option D is correct.