Triangle Classification Theorems

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

b. 10, 24, 26

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range possible values for the third side of the triangle?

b. 12.5 < x < 18.9

The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possible whole-number value of x?

b. 7

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

3.2 inches

The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tenth, what is the greatest possible value of x?

a. 6.3

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm, is a right triangle?

a. The triangle is a right triangle because 5^2 + 12^2 = 13^2

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

b. 6 < s < 12.8

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support bean that will connect the ends of the two boards measures 20 feet. Which is true regarding the triangular frame?

b. It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?

c. 72.44 in.

Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

c. The triangle is not acute because 2^2 + 4^2 < 5^2.

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

c. obtuse, because 6^2 + 10^2 < 12^2

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

d. 5.7 cm

The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

d. 8.5 cm

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

b. 5, 7, 8

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches. What is the greatest possible whole-number length of the unknown side?

7 inches