Question

solve for x.
a)

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(x\) and \(21\) are the legs, and \(28\) is the hypotenuse. So \(x^{2}+21^{2}=28^{2}\).

Step2: Simplify the equation

\(x^{2}=28^{2}-21^{2}\). Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\), we have \(x^{2}=(28 + 21)(28-21)=(49)(7)=343\).

Step3: Solve for \(x\)

\(x=\sqrt{343}=7\sqrt{7}\approx18.52\)

Answer:

\(x = 7\sqrt{7}\approx18.52\)