The longest side of an isosceles obtuse triangle measures 20 centimeters. the other two side lengths are congruent but unknown.

what is the greatest possible whole-number value of the congruent side lengths?

a.9 cm
b.10 cm
c.14 cm
d.15 cm

Since 9+9=19<20 and 10+10=20=20, the triangles with sides 9, 9, 20 and 10, 10, 20 cannot exist.

Use the cosine theorem to check which option C or D is true:

1.

.

You have that cosine of the greatest angle (opposite to the greatest side) is negative, this means that angle is obtuse.

2.

.

Here you have that cosine of the greatest angle (opposite to the greatest side) is posiative, this means that angle is acute.

the greatest possible whole-number value of the congruent side lengths is 14 (choice C)

step-by-step explanation: