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Each leg of an isosceles triangle is $15$ inches in length, and the altitude from the vertex angle to the base of the triangle is $10$ inches. Find the length of the base in inches.

A

$2\sqrt{5}$

B

$5\sqrt{5}$

C

$5\sqrt{13}$

D

$10\sqrt{5}$

E

$10\sqrt{13}$

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