math help again.?

Question

1. if the length of a leg of an isosceles right triangle is 20 cm.
find the legth of the hypothenese.

* my answer was h = 20 radical 2

am i right? if not show me the steps how to get this answer and explain please.

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2. find the altitude of an equilateral triangle who base is 5 cm.

* my answer was alttitude = 5?

if not, can you please explain and show me how how to get the answer?

Answer 1

#1: your answer is correct
#2: incorrect. The answer is (5√3)/2. The reason is as follows - drawing the altitude of an equilateral triangle divides it into two congruent right triangles, with a hypotenuse which is the length of any of the sides of the triangle (since it IS one of the sides of the triangle), and one leg of half that length (since it is the bisection of one of the other sides). The altitude itself is the other leg of the right triangle(s), and may be found from the pythagorean theorem - in this case, the hypotenuse is 5, so we have a²+(5/2)²=5² → a=5√3/2.