In an isosceles triangle, the perpendicular bisected of one leg passes thru the midpoint of the base. If the leg is 10, how long is the base?

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In an isosceles triangle, the perpendicular bisected of one leg passes thru the midpoint of the base. If the leg is 10, how long is the base?

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Answer 1 · 2018-03-27T23:56:08

20

Explanation:

if the diagram i have is correct then the answer is 20.
enter image source here
because
in $△ A D C$ $triangle ADC$ $∠ C$ $angle C$ is $90^{\circ}$ $90^@$ and $∠ D$ $angle D$ is $90^{\circ}$ $90^@$ so the $∠ D A C = 180 - 45 - 90 = 45^{\circ}$ $angle DAC = 180-45-90 = 45^@$
in an isosceles triangle the perpendicular from the top to the bottom will bisect the bottom line.
as $△ A D C$ $triangle ADC$ is a isosceles triangle $A D = D C$ $AD = DC$
so, $D C = 10$ $DC = 10$
therefore, the length of the total base is $10 + 10 = 20$ $10+10 =20$

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In an isosceles triangle, the perpendicular bisected of one leg passes thru the midpoint of the base. If the leg is 10, how long is the base?

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