Question

find the length of side ( x ) to the nearest tenth.

Explanation:

Step1: Identify triangle type

The triangle is isosceles right - angled (two equal sides, one right angle). Let the equal sides be \(x\) (legs), hypotenuse \(c = 3\).

Step2: Apply Pythagorean theorem

For a right - angled triangle, \(a^{2}+b^{2}=c^{2}\). Since \(a = b=x\), we have \(x^{2}+x^{2}=3^{2}\).
Simplify: \(2x^{2}=9\), then \(x^{2}=\frac{9}{2}\), so \(x=\sqrt{\frac{9}{2}}\).

Step3: Calculate and round

\(x=\frac{3}{\sqrt{2}}\approx\frac{3}{1.414}\approx2.1\) (rounded to the nearest tenth).

Answer:

\(2.1\)