Question

the triangle below is isosceles. find the length of side x to the nearest tenth.

answer attempt 1 out of 2

Explanation:

Step1: Identify triangle type

It's an isosceles right triangle, so legs are equal (\(x = \text{other leg}\)), hypotenuse \(c=\sqrt{11}\).

Step2: Apply Pythagorean theorem

For right triangle, \(a^2 + b^2 = c^2\). Here \(a = x\), \(b = x\), \(c=\sqrt{11}\). So \(x^2 + x^2 = (\sqrt{11})^2\).

Step3: Simplify equation

\(2x^2 = 11\) → \(x^2=\frac{11}{2}=5.5\).

Step4: Solve for \(x\)

\(x=\sqrt{5.5}\approx2.3\) (to nearest tenth).

Answer:

\(2.3\)