Question

find the length of the leg $x$. enter the exact value, not a decimal approximation.
$x=$
question help: post to forum
submit question jump to answer

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 15\), \(b = 12\), and we want to find \(a=x\). So, \(x^{2}+12^{2}=15^{2}\).

Step2: Rearrange the equation

We can rewrite the equation as \(x^{2}=15^{2}-12^{2}\).

Step3: Calculate the squares

\(15^{2}=225\) and \(12^{2}=144\). Then \(x^{2}=225 - 144\).

Step4: Subtract

\(x^{2}=81\).

Step5: Solve for \(x\)

Taking the square root of both sides, since \(x\) represents the length of a side of a triangle (a non - negative quantity), \(x=\sqrt{81}=9\).

Answer:

9