Mathematics
Is it possible to construct a quadrilateral with sides 5 cm, 6 cm, 7 cm, 8 cm and one of the diagonal 15 cm.
Yes
No
Nothing can be said
Answer
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.
Related Questions
Construct a rhombus, having given one side = 4.8 cm and one angle = 75°.
Construct a regular hexagon of side
(i) 2.5 cm
(ii) 3.2 cm
In a regular hexagon, leading diagonal of it, is twice of its side.
Yes
No
Nothing can be said
Statement 1: In a quadrilateral ABCD; AB = BC = CD = DA = 8 cm.
Statement 2: It is possible to construct the quadrilateral.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.