Question

in centimeters, what is the unknown length in this right triangle? 60 cm 61 cm x

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let \(a = 60\), \(c=61\), and \(b=x\). Then \(x^{2}+60^{2}=61^{2}\).

Step2: Rearrange the formula

\(x^{2}=61^{2}-60^{2}\). Using the difference of squares \(a^{2}-b^{2}=(a + b)(a - b)\), here \(a = 61\), \(b = 60\). So \(x^{2}=(61 + 60)(61 - 60)\).

Step3: Calculate the values

\((61 + 60)(61 - 60)=121\times1\). Then \(x^{2}=121\). Taking the square root of both sides, \(x=\sqrt{121}\).

Answer:

\(11\)