Question

find x.
15 cm
x
12 cm
x = centimeters
submit

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). In this triangle, the hypotenuse \(c = 15\space cm\), one leg \(b = 12\space cm\), and the other leg is \(x\). We can rewrite the Pythagorean theorem to solve for \(x\): \(x^{2}=c^{2}-b^{2}\)

Step2: Substitute the values

Substitute \(c = 15\) and \(b = 12\) into the formula: \(x^{2}=15^{2}-12^{2}\). Calculate \(15^{2}=225\) and \(12^{2}=144\). Then \(x^{2}=225 - 144=81\)

Step3: Solve for \(x\)

Take the square root of both sides: \(x=\sqrt{81}=9\)

Answer:

\(9\)