Question

GEOMETRY 50POINTS

determine what type of triangle they will form.

BRILLIANT for the best answer ​

Answer 1

acute triangle

Explanation:

for the given sides to form a triangle

the sum of any 2 sides must be greater than the third side

given 56 , 90 , 100

56 + 90 = 146 > 100

56 + 100 = 156 > 90

90 + 100 = 190 > 56

the condition is met so the 3 lengths will form a triangle.

let a = 56 , b = 90 and c = 100 , where c represents the longest of the 3 sides , then

• if a² + b² = c² , then triangle is right

• if a² + b² > c² , then triangle is acute

• if a² + b² < c² , then triangle is obtuse

a² + b² = 56² + 90² = 3136 + 8100 = 11,236

c² = 100² = 10, 000

since a² + b² > c² , then triangle is acute