Question

What will replace the question mark?

Answer 1

Hint: In this question, we need to determine the value that should be replaced with the question such that the values given in the preceding figures satisfy. For this, we will establish a relation between the vertices of the triangles.

Complete step-by-step answer:
From the first triangle in the figure, the three vertices of the triangle are 56, 5 and 9. We have to establish a relation which will be satisfying the values in the vertices of other succeeding triangles also.
So, from the first triangle we can say that the difference in the square of the base vertices results in the value of the top edge vertex such as
$
\Rightarrow {9^2} - {5^2} = 81 - 25 \\
   = 56 \\
 $
Similarly, from the second triangle in the figure, the three vertices of the triangle are 28, 6 and 8. So,
$
\Rightarrow {8^2} - {6^2} = 64 - 36 \\
   = 28 \\
 $
As the same condition is satisfying both the first and the second triangle, we can apply the same condition in the third triangle in which we need to determine the value of the question mark.
From the third triangle in the figure, the three vertices of the triangle are ?, 5 and 6. So,
$
\Rightarrow {6^2} - {5^2} = 36 - 25 \\
   = 11 \\
 $
Hence, the value of the question mark in the top vertex of the third triangle in the given figure is 11 following the condition that the difference in the square of the base vertices results in the value of the top edge vertex.

Note: In this type of questions, students need to establish a condition which satisfies all the mathematical representations. However, it is not always essential that a fixed mathematical condition is there to solve this type of question, it varies from person perspective.