Question

The 160 cm border for a triangular tail fin of a space vehicle is built from small ceramic rods. Each side of the triangular tail is built Using several small rods of equal length. One side of the tail fin must be exactly 56 cm long. So that ceramic rods do not have to be broken to fit the border and to meet aerodynamic constraints, the length of the other two sides must be in a ratio of 5:8. What are the links of the three side of the tail fin?using several small rods of equal length. One side of the tail fin must be exactly 56 cm long. So that ceramic rods do not have to be broken to fit the border and to meet aerodynamic constraints, the length of the other two sides must be in a ratio of 5:8. What are the lengths of the three sides of the tail fin?

Answer 1

Explanation:

To find the lengths of the three sides of the tail fin, we can use the information provided to set up a system of equations. Let's call the length of the side that is 56 cm long x, and let's call the length of the other two sides y and z.

We know that x = 56 cm and that y:z = 5:8. We can set up the following system of equations to represent these conditions:

x = 56

y:z = 5:8

We can also write this system of equations in terms of y and z:

x = 56

y + z = 13y/5

To solve this system of equations, we can first solve for y in the second equation:

y = (5/13)z

Substituting this expression for y into the first equation gives us:

56 = (5/13)z + z

This equation simplifies to:

56 = (18/13)z

Dividing both sides by (18/13) gives us:

z = 56 * (13/18) = 33.33 cm

Since y:z = 5:8, we know that y = (5/8) * z = (5/8) * 33.33 = 20.83 cm.

So, the lengths of the three sides of the tail fin are x = 56 cm, y = 20.83 cm, and z = 33.33 cm.