Question

consider the triangle. which statement is true about the lengths of the sides? each side has a different length. two sides have the same length, which is less than the length of the third side. the three sides have the same length. the sum of the lengths of two sides is equal to the length of the third side.

Explanation:

Step1: Determine the type of triangle

Since one angle is \(90^{\circ}\) (right - angle) and two other angles are \(45^{\circ}\) each, this is a \(45 - 45-90\) triangle.

Step2: Recall the properties of a \(45 - 45 - 90\) triangle

In a \(45 - 45-90\) triangle, the legs are equal. Let the length of each leg be \(a\). By the Pythagorean theorem \(c^{2}=a^{2}+a^{2}\) (where \(c\) is the hypotenuse), so \(c = a\sqrt{2}\).

Answer:

Two sides have the same length, which is less than the length of the third side.