Question

35 63 56 48 54 ?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). In the first triangle, \(35^{2}+56^{2}=1225 + 3136=4361\) and \(63^{2}=3969\), this is not a right - triangle. But if we assume the two triangles are similar. For similar triangles, the ratios of corresponding sides are equal. Let the unknown side of the second triangle be \(x\). We have the proportion \(\frac{35}{48}=\frac{56}{54}=\frac{63}{x}\). First, check \(\frac{35}{48}
eq\frac{56}{54}\). Let's use the Pythagorean theorem for the second triangle. If it's a right - triangle, \(x=\sqrt{48^{2}+54^{2}}\).

Step2: Calculate squares

Calculate \(48^{2}=48\times48 = 2304\) and \(54^{2}=54\times54=2916\).

Step3: Sum the squares

\(2304 + 2916=5220\).

Step4: Find the square - root

\(x=\sqrt{5220}=6\sqrt{145}\approx72.25\).

Answer:

\(72.25\)