Question

1. 45 43 $x^{2}$ ?

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 45\), \(a=x\), and \(b = 43\). So, \(x^{2}+43^{2}=45^{2}\).

Step2: Rearrange to solve for \(x^{2}\)

\(x^{2}=45^{2}-43^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(45 + 43)(45-43)\).

Step3: Calculate the values

\(45+43 = 88\) and \(45 - 43=2\). Then \(x^{2}=88\times2=176\).

Answer:

\(x^{2}=176\)