Question

c = 3; d = 3
c = 3√3; d = 4√3
c = 4√3; d = 4√3
c = 6√2; d = 6√2

Explanation:

Step1: Recognize the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal (\(c = d\)), and the hypotenuse \(h\) is related to the legs \(l\) by the formula \(h=\sqrt{2}l\).

Step2: Solve for the legs

Given \(h = 12\), from \(h=\sqrt{2}l\), we can solve for \(l\) (where \(l\) represents both \(c\) and \(d\)). Rearranging the formula gives \(l=\frac{h}{\sqrt{2}}\). Rationalizing the denominator: \(l=\frac{12}{\sqrt{2}}=\frac{12\sqrt{2}}{2}=6\sqrt{2}\).

Answer:

\(c = 6\sqrt{2};d = 6\sqrt{2}\) (the fourth option)