Question

Sasha says that she drew an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100°. Danielle says that is not possible. Explain, using sides and angles, who is correct.

Answer 1

Danielle is correct that it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100°.

Solution:

Given that,

Sasha says that she drew an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100°

Given that she drew a acute isosceles triangle

Let us understand about isosceles triangle

An isosceles triangle is a triangle with (at least) two equal sides and also two of the angles are equal.

But given sides are of length 6 cm, 9 cm and 12 cm

Therefore, all sides are of different length. So it does not form a isosceles triangle

Given that she drew a acute isosceles triangle

Let us understand about acute angle

An acute triangle has three angles that each measure less than 90 degrees.

For any acute isosceles triangle two sides and two angles are equal .Each angle is less than 90 degrees.

But given angles measure 30°, 50°, and 100°

Here, one angle is greater than 90 degrees and any two angles are not equal.

Therefore, all angles measure different degrees, so they cannot form a acute isosceles triangle

Thus Danielle is correct that it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100°.