Question

You want to make 3 pairs of earrings that are in the shape of isosceles triangles. Each earring will have a base of 2 cm. The wire to make the earrings is 50 cm long. If you want to maximize the use of the wire, which of the following would represent the length of each of the other two sides?

Answer 1

3 cm

Explanation:

If there are 3 pairs, that means 6 earrings in total and if all of the bases are 2 then there is already a total of 12 cm of wire being used but there are 12 sides that you still don't know. So what you do is subtract 50 by 12 to get 38 then you divide 38 by twelve to get 3.16. Then you would round down.

Answer 2

3.1 cm

Explanation:

We are given that

Total pairs of earrings=3

Total number of isosceles triangles=
`3* 2=6`

Length of base=2 cm

Length of wire used=50 cm

We have to find the length of each of the other two sides of isosceles triangle.

Let x be the length of each of two equal sides of isosceles triangle.

Perimeter of one isosceles triangle=Sum of length of three sides =
`x+x+2=2x+2`

Perimeter of 6 isosceles triangle=
`6*(2x+2)=12x+12`

Perimeter of 6 isosceles triangle
`\leq` Length of wire used

Substitute the values

`12x+12\leq 50`

`12x \leq50-12=38`

`x \leq (38)/(12)=3.16`

`x=3.1`

Hence, the length of each of the other two sides of isosceles triangle=3.1 cm