The perimeter of a triangle is 50. The length of the sides of a smaller, similar triangle are 5, 6, and 9. FInd the sides of the larger triangle. What steps would I take to solve this?
Every question above mine is answered. Did anyone take the time to read this? I don't even want a solution just the steps I need.
Add up 5+6+9 = 20
the larger triangle has a perimeter 50/20 as big, so each of its sides will be 50/20 as big as the corresponding sides of the smaller triangle.
To solve this problem, we can set up a proportion between the corresponding sides of the two triangles. Here are the steps you can follow:
Step 1: Understand the problem and identify the given information:
- There are two triangles, a smaller triangle, and a larger, similar triangle.
- The perimeter of the larger triangle is given as 50.
- The sides of the smaller triangle are given as 5, 6, and 9.
Step 2: Understand similar triangles:
- Similar triangles are triangles that have the same shape, but not necessarily the same size.
- Corresponding sides of similar triangles have the same ratio.
Step 3: Set up a proportion between the corresponding sides of the two triangles:
- Since the triangles are similar, we can set up a proportion using the corresponding sides.
- Let's call the sides of the larger triangle as x, y, and z.
Step 4: Write down the proportion equation:
- The proportion equation for the sides of the two triangles can be written as:
x/5 = y/6 = z/9.
Step 5: Simplify the proportion equation:
- Multiply all terms by the least common multiple (LCM) of 5, 6, and 9, which is 90, to eliminate the denominators.
- This gives us:
90*(x/5) = 90*(y/6) = 90*(z/9) = 90x/5 = 90y/6 = 90z/9.
Step 6: Express the sides of the larger triangle in terms of a common ratio:
- Simplify each expression:
18x = 15y = 10z.
Step 7: Use the given information about the perimeter of the larger triangle:
- The perimeter of the larger triangle is given as 50.
- Apply this information to the sides of the larger triangle:
x + y + z = 50.
Step 8: Solve the system of equations:
- We can solve the system of equations consisting of 18x = 15y = 10z and x + y + z = 50 to find the values of x, y, and z.
By following these steps, you should be able to find the lengths of the sides of the larger triangle.