Solving for Triangle Sides with Algebra

Which set of sides would make a right triangle?

• 4,5,6
• 8,10,12
• 5,12,13
• 5,10,12

A triangle has the following side lengths: 
AB = 12 units
BC = 10 units
AC = 16 units 
What type of triangle does this make?

• Acute
• Obtuse
• Right
• Equilateral 

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet
• 26 feet
• 27 feet
• 28 feet

A triangle has side lengths:
8, 8√3, 16  .  Is this triangle a right triangle, an acute triangle, or an obtuse triangle?

• right
• acute
• obtuse

• x = 7, y = 7√2
• x = 14 y = 7√2
• x = 14√2 y = 7√2
• x = 14 y = 14√2

• a = 5, b = 5
• a = 10, b = 10√2
• a = 10√2, b = 10√2
• a = 5√2, b = 5√2

• v = 9√3, u = 6√3
• v = 6√3 u = 9√3
• v = 9, u = 6√3
• v = 3√6, u = 6√3

• x = 3, y = 6
• x = 6√2, y = 12√2
• x = 2√3, y = 4√3
• x = 3√2, y = 6√2

• 20
• 5.9
• 33
• 42

• x=18
• x=18√3
• x=36√3
• x=12