Final answer:
The length of the smallest side of a triangle with sides in the ratio of 1/2:1/3:1/4 and a perimeter of 52 cm, we express the ratios with a common denominator, set up an equation, solve for the common multiplier, and apply it to the smallest ratio, resulting in 12 cm.
Step-by-step explanation:
The question asks for the length of the smallest side of a triangle whose sides are in the ratio of 1/2:1/3:1/4 and the perimeter is 52cm. First, we will find a common denominator for the ratios, which is 12 in this case. Thus, we can express the ratios as 6:4:3. Now, let's set up an equation where x is a common multiplier for these ratios:
6x + 4x + 3x = 52
Thus, 13x = 52, so x = 52/13, which means x = 4. Applying our multiplier to the smallest ratio (which is 3x), we find that the smallest side is 3*4 = 12 cm. Therefore, the correct answer is D) 12 cm.