Is it possible to construct a quadrilateral with sides 5 cm, 6 cm, 7 cm, 8 cm and one of the diagonal 15 cm.

1. Yes

2. No

3. Nothing can be said

A quadrilateral with a diagonal forms two triangles. Let the diagonal be 15 cm.

Consider one triangle with sides 5 cm, 6 cm, and 15 cm.

Consider the other triangle with sides 7 cm, 8 cm, and 15 cm.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Check if the sum of any two sides is greater than the third side for the triangle with sides 5 cm, 6 cm, and 15 cm.

Sum of 5 cm and 6 cm: 5 + 6 = 11.

Compare to the third side: 11 < 15.

Sum of 6 cm and 11 cm: 6 + 11 = 17.

Compare to the third side: 17 > 5.

Sum of 5 cm and 11 cm: 5 + 11 = 16.

Compare to the third side: 16 > 6.

Since 11 < 15, the Triangle Inequality Theorem is violated for the first triangle.

Therefore, a triangle with sides 5 cm, 6 cm, and 15 cm cannot be formed.

Thus, the quadrilateral cannot be constructed.

Hence, option 2 is the correct option.