In Delta ABC,m angle B = 90^{circ} and overli | vedclass

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(B) In a right-angled triangle,the altitude drawn from the right-angle vertex to the hypotenuse divides the triangle into two triangles that are simil

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(B) In a right-angled triangle,the altitude drawn from the right-angle vertex to the hypotenuse divides the triangle into two triangles that are similar to the original triangle and to each other.By the property of geometric mean in a right triangle,the altitude $BD$ to the hypotenuse $AC$ satisfies the relation:$BD^2 = AD 	imes CD$Given $AD = 9$ and $CD = 4$,we have:$BD^2 = 9 	imes 4$$BD^2 = 36$Taking the square root on both sides:$BD = \sqrt{36} = 6$Thus,the length of $BD$ is $6$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $AC$. If $AD = 9$ and $CD = 4$,find $BD$.

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