Question

Which dimensions cannot create a triangle? a three sides measuring 6 cm, 8 cm, and 10 cm b three angles measuring 40 degrees, 70 degrees, and 65 degrees c three angles measuring 10 degrees, 25 degrees, and 145 degrees d three sides measuring 9 m, 15 m, and 9 m

Answer 1

C

All triangle must equal 180, 40 + 70 + 65 = 175

Answer 2

A,C,D are triangles, B is not.

Explanation:

Let 3 sides of a triangle be a,b,c.

A triangle have the sum of 3 angles = 180 degree

and

a-b<c<a+b (similar for a and b)

a. three sides measuring 6 cm, 8 cm, and 10 cm

Satisfied the a-b<c<a+b property -> triangle

b. three angles measuring 40 degrees, 70 degrees, and 65 degrees

Total of 3 angles = 40+70+65 = 175 > 180

-> not triangle

c. three angles measuring 10 degrees, 25 degrees, and 145 degrees

Total of 3 angles = 10+25+145 = 180

-> triangle

d. three sides measuring 9 m, 15 m, and 9 m

Satisfied the a-b<c<a+b property -> triangle