Question

? 48 54 63 35 56

Explanation:

Step1: Apply the Pythagorean theorem for right - angled triangles.

For the right - angled triangle with sides 35, 56, and 63, we know that in a right - angled triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse.
For the other triangle with sides 48 and 54, let the unknown side be \(x\).

Step2: Calculate using the Pythagorean theorem.

If the triangle is a right - angled triangle, assume \(x\) is the hypotenuse, then \(x=\sqrt{48^{2}+54^{2}}\).
First, calculate \(48^{2}=48\times48 = 2304\) and \(54^{2}=54\times54=2916\).
Then \(48^{2}+54^{2}=2304 + 2916=5220\). So \(x=\sqrt{5220}\approx72.25\) (not an integer).
Let's assume the side we want to find is not the hypotenuse. If 54 is the hypotenuse, then \(x=\sqrt{54^{2}-48^{2}}=\sqrt{(54 + 48)(54 - 48)}=\sqrt{102\times6}=\sqrt{612}\approx24.74\) (not an integer).
If we consider the similarity of triangles.
The ratios of the sides of the second triangle are \(35:56:63 = 5:8:9\).
For the first triangle, if we assume the same ratio - like relationship.
Let's check if the first triangle is a multiple of some basic right - angled triangle.
We know that \(48 = 6\times8\) and \(54=6\times9\), so the missing side should be \(6\times5 = 30\).

Answer:

30