Question

which triangles unknown side length measures 7 units?

Explanation:

Step1: Apply Pythagorean theorem for each triangle

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side of a right - triangle) and \(a\) and \(b\) are the other two sides.

First triangle:

Let the unknown side be \(x\). Here \(x^{2}+(\sqrt{2})^{2}=4^{2}\).

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Second triangle:

Let the unknown side be \(y\). Here \(y^{2}+5^{2}=(\sqrt{74})^{2}\).

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Third triangle:

Let the unknown side be \(z\). Here \(z^{2}+(\sqrt{18})^{2}=5^{2}\).

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Fourth triangle:

Let the unknown side be \(w\). Here \(w^{2}+(\sqrt{6})^{2}=(\sqrt{43})^{2}\).

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Answer:

The second triangle (the one with sides \(5\) and \(\sqrt{74}\)) has an unknown side length of \(7\) units.