Question

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Explanation:

Step1: Apply Pythagorean theorem for left - triangle

For a right - triangle with legs \(a = 27\) and \(b = 36\), the hypotenuse \(x\) is calculated by \(x=\sqrt{a^{2}+b^{2}}\). So \(x=\sqrt{27^{2}+36^{2}}=\sqrt{729 + 1296}=\sqrt{2025}=45\).

Step2: Apply Pythagorean theorem for right - triangle on right

For a right - triangle with legs \(a = 10\) and \(b = 24\), the hypotenuse \(x\) is calculated by \(x=\sqrt{a^{2}+b^{2}}\). So \(x=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26\).

Answer:

For the left - triangle, \(x = 45\); for the right - triangle, \(x = 26\)