Final answer:
To find the lengths of the sides of a triangle with an extended ratio of 7:9:10 and a perimeter of 52 cm, represent the sides as 7x, 9x, and 10x. Solve for x using the perimeter and then multiply each term of the ratio by x to obtain the side lengths: 14 cm, 18 cm, and 20 cm.
Step-by-step explanation:
The question involves finding the length of the sides of a triangle when given the extended ratio and the perimeter. To solve this, we can represent the lengths of the sides by 7x, 9x, and 10x, where x is a common multiplier. The extended ratio 7:9:10 indicates that the lengths of the triangle's sides are proportional to these numbers. Since the perimeter is the sum of all three sides, we can write the equation 7x + 9x + 10x = 52.
By simplifying, we combine the like terms, obtaining 26x = 52. Dividing both sides by 26 gives us the value of x, which is 2. Now, we multiply the ratio numbers by x to find the actual lengths: 7x = 14 cm, 9x = 18 cm, and 10x = 20 cm. Thus, the lengths of the sides of the triangle are 14 cm, 18 cm, and 20 cm respectively.