Question

For a craft project, four students each chose three pieces of wire from a box.

Don’s wires measure 3 inches, 5 inches, and 12 inches.
Margo’s wires measure 6 inches, 8 inches, and 14 inches.
Sonji’s wires measure 12 inches, 8 inches, and 17 inches.
Liam’s wires measure 16 inches, 8 inches, and 27 inches.

Which student chose pieces that can be used to construct a triangle?

Don
Margo
Sonji
Liam

Answer 1

Sonji's.

The third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other twosides and greater than the difference of the lengths of the other two sides.

Answer 2

Sonji

Explanation:

Given :

We will use the third important property of triangles is the triangle inequality rule, which states: the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

So, applying this property in each case:

Case 1. Don’s wires measure 3 inches, 5 inches, and 12 inches.

Now using property

since sum of two sides = 3+5 =8

But third side 12 is not less than 8

So, Don’s wire cannot be used .

Case 2. Margo’s wires measure 6 inches, 8 inches, and 14 inches.

Now using property

since sum of two side :8+6=14

But third side 14 is not less than 14

So, Margo’s wire cannot be used .

Case 3. Sonji’s wires measure 12 inches, 8 inches, and 17 inches.

Now using property

since sum of two side :12+8=20

third side 17 is less than 20

Now , difference of two sides : 12-8=4

third side 17 is greater than 4

So, Sonji’s wire can be used .

Case 4. Liam’s wires measure 16 inches, 8 inches, and 27 inches.

Now using property

since sum of two side :16+8 =24

But third side 27 is not less than 24

So, Liam’s wire cannot be used .

Hence sonji's wire can be used to construct a triangle