Final answer:
To find the length of the side labeled x in similar shapes with a perimeter ratio of 7:10 and one side length of 12, set up the proportion 12/7 = x/10, cross multiply, and solve for x, resulting in approximately 17.14 units.
Step-by-step explanation:
The student is asking how to find the length of a side labeled x in similar shapes, given the ratio of the perimeters is 7:10 and that one side of one shape is 12 units long. To solve for x, one must set up a proportion based on the given ratio. Here is the step-by-step solution:
- Establish the ratio of the perimeters of similar shapes, which is given as 7:10.
- Understand that corresponding sides of similar shapes are in the same ratio as their perimeters. Therefore, if one side in the smaller shape is 12, then the corresponding side (x) in the larger shape can be calculated by setting up the proportion 12/7 = x/10 based on the perimeter ratio.
- Cross multiply to solve for x: 12 * 10 = 7 * x.
- From the cross multiplication 120 = 7x, divide both sides by 7 to isolate x: x = 120/7.
- Calculate the value to find x: x ≈ 17.14 (rounded to two decimal places).
After carrying out these steps, the value of the side labeled x in the larger shape is approximately 17.14 units.