Question

find the length of side x to the nearest tenth.

(right triangle with legs x (marked with one tick) and another leg (marked with one tick, so equal to x), hypotenuse √10)

answer attempt 1 out of 2
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Explanation:

Step1: Identify triangle properties

This is an isosceles right triangle: the two legs (one labeled $x$, the other congruent to it) form the right angle, and the hypotenuse is $\sqrt{10}$.

Step2: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $a=b=x$, $c=\sqrt{10}$.
$$x^2 + x^2 = (\sqrt{10})^2$$

Step3: Simplify the equation

Combine like terms and compute the hypotenuse squared:
$$2x^2 = 10$$

Step4: Solve for $x^2$

Divide both sides by 2:
$$x^2 = \frac{10}{2} = 5$$

Step5: Solve for $x$

Take the square root of both sides:
$$x = \sqrt{5} \approx 2.2$$

Answer:

$2.2$