Question

which right triangles unknown leg measure is √43 units? assume the given lengths are in the same unit of measure.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Check the first triangle

Let the unknown leg be \(x\). Given \(c = 12\), \(b=\sqrt{44}\). Then \(x^{2}+(\sqrt{44})^{2}=12^{2}\), \(x^{2}+44 = 144\), \(x^{2}=144 - 44=100\), \(x = 10
eq\sqrt{43}\).

Step3: Check the second triangle

Let the unknown leg be \(y\). Given \(c=\sqrt{90}\), \(a = 6\). Then \(y^{2}+6^{2}=(\sqrt{90})^{2}\), \(y^{2}+36=90\), \(y^{2}=90 - 36 = 54\), \(y=\sqrt{54}
eq\sqrt{43}\).

Step4: Check the third triangle

Let the unknown leg be \(z\). Given \(c=\sqrt{60}\), \(a=\sqrt{19}\). Then \(z^{2}+(\sqrt{19})^{2}=(\sqrt{60})^{2}\), \(z^{2}+19 = 60\), \(z^{2}=60 - 19=41\), \(z=\sqrt{41}
eq\sqrt{43}\).

Step5: Check the fourth triangle

Let the unknown leg be \(w\). Given \(c = 8\), \(b=\sqrt{21}\). Then \(w^{2}+(\sqrt{21})^{2}=8^{2}\), \(w^{2}+21=64\), \(w^{2}=64 - 21 = 43\), \(w=\sqrt{43}\).

Answer:

The fourth right - triangle.