equilateral triangle?

Question

i need homework. i am stuck on this one problem.

the side of an equilateral triangle is 10cm. the altitude of the triangle forms a right angle with the base. find the length of the altitude.

answers a) 5cm b) 5squareroot 3 c) 5squareroot5

and thats all it gives me.

also, how would i work this problem out?

Answer 1

OK, here goes -

All sides are 10cm.
You have basically drawn a line from the center of the base up to the top of the triangle, since you state that this line is the altitude (highest point). Since the line is in the center, the other side of the right triangle is 5cm. The hypotenuse is 10cm.

From the Pythagorean Theorem, 10^2 = 5^2 + x^2. We know we can use this since we have formed a right triangle.

100 = 25 + x^2
75 = x^2
X = sqrt 75 but we know that 5 is a factor twice in 75 (5*5*3), so the answer is 5 sqrt 3, or b).

Answer 2

Start with the Pythagorean Theorem: a^2 + b^2 = c^2.

C (the hypotenuse) is 10. We know this from the length of the sides of the equilateral triangle.

B (base) is 5. We know this because when you drop a perpendicular line from the peak of an equilateral triangle, it bisects the opposite side. It also produces two right triangles, which is why we can use the Pythagorean Theorem. :-)

So, we just plug the numbers back in and solve for A:

a^2 + b^2 = c^2
a^2 + 5^2 = 10^2
a^2 + 25 = 100
a^2 = 75
a = sqrt (75) = sqrt (5*5*3) = 5 * sqrt(3).

Answer 3

equilateral triangle means all sides are equal. so all three sides are 10 cm. the altitude forms a right angle with the base. so it is 90 degrees. the altitude cuts the base in half.

use pythagorean theorem x ^2 + 5^2 = 10^2 (in case you dont know ^2 means squared)
x^2=100-25
x^2=75
x= square root of 75
x=5 square root of 3
(b)

Answer 4

If you take your equilateral triangle and cut it in half along the altitude, you will end up with a ttriangle of sides x, 2x, and x root 3.
X is the base, or half of the original side.
2x is now the hypotonose
and X root 3 is the height.

Can you figure it out from there?

Answer 5

answer is 5 square root 3

Answer 6

B is the right answer

Answer 7

b is the right answer!

Answer 8

b