Question

ur answer to decimal form. draw 45° 16 x ork here he square root symbol (√□), type
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Explanation:

Step1: Identify the triangle type

This is a right - angled isosceles triangle (since one angle is \(45^{\circ}\), the other non - right angle is also \(45^{\circ}\)). In a right - angled isosceles triangle, the legs are equal. Let the legs be \(a\) and \(b\), and the hypotenuse \(c\). By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), and since \(a = b=x\), we have \(2x^{2}=c^{2}\).

Step2: Substitute the value of the hypotenuse

Given \(c = 16\), then \(2x^{2}=16^{2}\). So \(2x^{2}=256\), and \(x^{2}=\frac{256}{2}=128\).

Step3: Solve for \(x\)

\(x=\sqrt{128}\). Simplify \(\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}\approx8\times1.414 = 11.312\)

Answer:

\(11.312\)