SOLUTION: Find the length of the altitude to the base of an isosceles triangle which has congruent legs of length 25 cm and a base of length 14 cm

Question 1096782: Find the length of the altitude to the base of an isosceles triangle which has congruent legs of length 25 cm and a base of length 14 cm
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
An isosceles triangle has two sides of equal length and the altitude drawn to the
base bisects the triangle's base
:
let s be the length of one of the equal sides, a be the length of the altitude and b be the length of the triangle's base then use Pythagorean theorem for a right triangle
:
a^2 + (b/2)^2 = s^2
:
we are given, s = 25 and b = 14
:
a^2 + (14/2)^2 = 25^2
:
a^2 + 49 = 625
:
a^2 = 576
:
a = 24 or -24
:
we reject the negative value for a
:
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the isosceles triangle's altitude is 24 cm
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