Question

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

Options

• Yes

• No

• Nothing can be said

Answer 1

No

Explanation:

A diagonal divides a quadrilateral into two triangles. For the triangle formed by the sides of lengths 5 cm, 6 cm, and a diagonal of 15 cm, we check the triangle inequality theorem (the sum of any two sides must be greater than the third side):

5 + 6 = 11 ≯ 15

Since 11 is not greater than 15, a triangle with these side lengths cannot exist, making it impossible to construct such a quadrilateral.