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(B) In a right-angled triangle,the altitude to the hypotenuse creates two triangles that are similar to the original triangle and to each other.By the

Vedclass · Accepted Answer

$6$

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(B) In a right-angled triangle,the altitude to the hypotenuse creates two triangles that are similar to the original triangle and to each other.By the Geometric Mean Theorem (or properties of similar triangles),we have the relationship: $YZ^2 = ZM \cdot XZ$.First,calculate the total length of the hypotenuse $XZ$:$XZ = XM + ZM = 5 + 4 = 9$.Now,substitute the values into the formula:$YZ^2 = 4 \cdot 9 = 36$.Taking the square root of both sides:$YZ = \sqrt{36} = 6$.Thus,the length of $YZ$ is $6$.

In $\Delta XYZ$,$m \angle Y = 90^\circ$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $XM = 5$ and $ZM = 4$,find $YZ$.

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