Question

type the correct answer in the box. a printer creates a right - triangular card where the hypotenuse, h, is three times as long as the shorter leg. what is the length of the longer leg, l, in terms of h? write the answer in simplest form by replacing a, b, and c with the correct values. c = a√(bh)

Explanation:

Step1: Recall Pythagorean theorem

Let the shorter leg be \(a\), the longer leg be \(c\), and the hypotenuse be \(h\). In a right - triangle, \(h^{2}=a^{2}+c^{2}\). Given \(h = 3a\).

Step2: Substitute \(h\) into Pythagorean theorem

\((3a)^{2}=a^{2}+c^{2}\), which simplifies to \(9a^{2}=a^{2}+c^{2}\).

Step3: Solve for \(c\)

Subtract \(a^{2}\) from both sides: \(c^{2}=9a^{2}-a^{2}=8a^{2}\). Then \(c = \sqrt{8a^{2}}=2\sqrt{2}a\).

Answer:

\(2\sqrt{2}a\)