Question

Which dimensions can create only one unique triangle?

A.Three angles measuring 75,45,and 50
B.Three sides measuring 14 m,11 m,and 18 m
C.Three angles measuring 40,50 and 60
D.Three sides measuring 3 cm,4 cm,and 8 cm

Answer 1

The correct answer is B.

Good luck!!!

Answer 2

Answer: B.Three sides measuring 14 m,11 m,and 18 m

Explanation:

Let's check all the option.

A. Three angles measuring 75,45,and 50

We know that the sum of all angles of a triangle is 180°.

But
`75+45+50=170` Therefore triangle is not possible with this dimensions of angles.

B. Three sides measuring 14 m,11 m,and 18 m

• For a unique triangle, the triangle inequality says that the sum of any two sides of a triangle must be greater than the third side.

Here ,

`14+11=25>18\\18+14=32>11\\11+18=29>14`

⇒ It satisfies the triangle inequality.

∴ There is one unique triangle of dimensions 14 m,11 m,and 18 m

.

C.Three angles measuring 40,50 and 60.

.

But
`40+50+60=150` Therefore triangle is not possible with this dimensions of angles.

D.Three sides measuring 3 cm,4 cm,and 8 cm

Here ,
`3+4=7<8`

Hence, it does not satisfies the triangle inequality.