Question

Which measurement could create more than one triangle? A.? A triangle with sides measuring 5 inches, 7 inches, 9 inches B. A triangle with sides measuring 50 mm 35 mm and a non-included angle measuring 25° C. A triangle with sides measuring 5 cm, 10 cm, and 15 cm D. A triangle with sides measuring 8 cm and 12 cm in an included angle measuring 85°

Answer 1

Answer: B. A triangle with sides measuring 50 mm 35 mm and a non-included angle measuring 25° .

Step-by-step explanation:

A. A triangle with sides measuring 5 inches, 7 inches, 9 inches

Only one triangle can be possible because all the triangles with equal sides must be equal by SSS congruence rule.

B. A triangle with sides measuring 50 mm ,35 mm and a non-included angle measuring 25°.

More than one triangle can be possible because there is no congruence rule for two equal sides and one non-equal angle ( no SSA rule exist).

C. A triangle with sides measuring 5 cm, 10 cm, and 15 cm .

This triangle is not possible because it doesn't satisfy triangle's inequality as 5+10=15  [Triangles inequality : a+b> c, where a, b, c are sides of triangle]

D. A triangle with sides measuring 8 cm and 12 cm in an included angle measuring 85°.

Only one triangle can be possible because all the triangles have two equal sides and their included angle is equal by SAS congruence rule.

Hence, the required measurement to create more than one triangle:

A triangle with sides measuring 50 mm 35 mm and a non-included angle measuring 25° .

So, correct option is B.