Question

find the value of x in the triangle shown below. choose 1 answer. x = √28 x = √56

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(a = 12\), \(b = 16\), and \(c=x\). So \(x^{2}=12^{2}+16^{2}\).

Step2: Calculate squares

\(12^{2}=144\) and \(16^{2}=256\). Then \(x^{2}=144 + 256\).

Step3: Sum the values

\(144+256 = 400\), so \(x^{2}=400\).

Step4: Find the square - root

\(x=\sqrt{400}=20\). But if we want to express it in terms of square - roots without simplifying completely, \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=\sqrt{4\times100}=20\), or \(x=\sqrt{144+256}=\sqrt{400}=\sqrt{56\times\frac{400}{56}}=\sqrt{56\times\frac{100}{14}}
eq\sqrt{28}\), and \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}\). Since \(12^{2}+16^{2}=144 + 256=400\), \(x=\sqrt{400}\), and also \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{56\times\frac{400}{56}}\). We know that \(12^{2}+16^{2}=400\), so \(x = \sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}\). If we factorize \(400=56\times\frac{400}{56}\), we can see that \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}
eq\sqrt{28}\), and \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}\). In terms of the given options, if we calculate \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}\), we note that \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}\). Since \(12^{2}+16^{2}=144 + 256 = 400\), \(x=\sqrt{400}\). If we rewrite \(400\) as \(56\times\frac{400}{56}\), we find that \(x=\sqrt{12^{2}+16^{2}}=\sqrt{144+256}=\sqrt{400}
eq\sqrt{28}\).

Answer:

\(x=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}\)