Side Length Relationship in Triangles

Fiona's school is in the shape of a triangle, with three hallways connecting the corners. Fiona enters the building and walks 90 yards through the first hallway to the first corner. Then, she walks 60 yards through the second hallway to the second corner.

What are the possible lengths of the third hallway?

• between 30 yards and 60 yards

• between 30 yards and 90 yards

• between 30 yards and 120 yards

• between 30 yards and 150

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?

• 4x < h < 10x

• 10x < h < 4x

• h = 4x

• h = 10x

The isosceles triangle has a base that measures 14 units.

The value of y, the length of each leg, must

• equal to 7.

• between 7 and 14.

• greater than 7

• between 14 and 28.

The value of x must be greater than ________.

• 0

• 1

• 3

• 7

Which inequality explains why these three segments cannot be used to construct a triangle?

• EF + FD > DE

• ED + EF < DF

• ED + EF > DF

• EF + FD < DE

Iliana claims that she can construct a triangle from a 12-inch rod, a 36-inch rod, and a 39.4-inch rod. Which statement explains whether she is correct?

• Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.

• Iliana cannot construct a triangle because the sum of the two smaller sides will be greater than the third side.

• Iliana will be able to construct a triangle because the sum of any two sides is greater than the third side.

• Iliana will be able to construct a triangle because the sum of any two sides is less than the third side.

Which statements about the diagram are true? Select three options.

• DE = EF > DF

• Triangle DEF is an isosceles triangle

• 5 < DF < 13

• DE + DF < EF

• Triangle DEF is a scalene triangle

Which inequality can be used to explain why these three segments cannot be used to construct a triangle?

• AC + AB > CB

• AC + CB < AB

• AC + CB > AB

• AC + AB < CB

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

Which are the possible side lengths of a triangle?

• 3 cm, 5 cm, 9 cm

• 4 cm, 8 cm, 10 cm

• 6 cm, 9 cm, 17 cm

• 8 cm, 10 cm, 18 cm