Question

elena wants to create a second triangular garden that is similar to the first, but the diagonal path must be exactly 15 ft long. if the shorter leg of the new garden is 9 ft, what must be the length of the longer leg? the length of the longer leg is ft. hide math input basic symbols greek other

Explanation:

Step1: Apply Pythagorean theorem

Let the longer leg be \(x\). For a right - triangle (garden with diagonal as hypotenuse), by Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 9\) (shorter leg), \(b=x\) (longer leg), \(c = 15\) (hypotenuse). So \(9^{2}+x^{2}=15^{2}\).

Step2: Simplify the equation

\(81+x^{2}=225\). Then \(x^{2}=225 - 81\).

Step3: Calculate \(x^{2}\)

\(x^{2}=144\).

Step4: Solve for \(x\)

Take square root of both sides, \(x=\sqrt{144}\), \(x = 12\).

Answer:

12