Question

one leg of a right triangle is 5 centimeters longer than the other leg. what quadratic inequality represents the length of the shorter leg, x, when the hypotenuse is at least 13 centimeters long? (1 point) $x^{2}+(x + 5)^{2}leq13^{2}$ $x^{2}+(x + 5)^{2}geq13^{2}$ $x^{2}+(5x)^{2}<13^{2}$ $x^{2}+(5x)^{2}geq13^{2}$

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, if the legs are \(x\) and \(x + 5\), and the hypotenuse \(c\), then \(a^{2}+b^{2}=c^{2}\) (for right - triangles). We know that \(c\geq13\), so \(x^{2}+(x + 5)^{2}\geq13^{2}\).

Answer:

\(x^{2}+(x + 5)^{2}\geq13^{2}\)