Word Problems - Math?

Question

I have to find the altitude of a triangle With (X) being the variable that represents the altitude of the triangle and solving for (X) I need to express my answer in both "simplified radical" and "decimal form"

The sides of the triangle are 13, 13, and 10

The problem is I dont know how to do it !! Please help !

Answer 1

OK... two sides of your triangle are 13, right?

So, lets cut the triangle in half, by splitting it down the middle. (draw it out on a piece of paper)

Now, you will have two triangles that look exactly the same, except, now they have a hypotenuse of 13, and the bottom is only 5 lengths long!

Plug this into the triangle formula:

a2 + b2 = c2

where c = 13, a=5 and b is the other side of the triangle (which is also the height of the original triangle)

so, c squared = 169 and 5 squared = 25

b2 = c2 - a2

b2 = 169-25

b2 = 144

b = 12

the height is 12, which i believe is the answer in both forms.

Answer 2

This is an isosceles triangle since it has two sides = 13
Using 10 as the base, then the altitude = sqrt(13^2-5^2)=
sqrt(169-25) = sqrt(144)=12.

Draw the triangle ABC with AB = 10 and AC = BC = 13.
Then draw a line from C perpendicular to AB at D. Then AD = 1/2 AB = 5. So you have a right triangle ACD with hypotenuse = 13 and short leg = 5 and the altitude being the other leg. Solve for the altitude using the pythagorean theorem and get 12 as I did above.

There are no radicals and if you want a decimal you could say 12.0 instead of 12.

Answer 3

This is an isosceles triangle.

So the base is 10, the sides are 13.

The altitide will split this isosceles triangle into two right triangles, each with a base of 5 and a hypoteneuse of 13.

The altitude is then 12, assuming you recognize this as a 5-12-13 Pythagorean triangle.

Answer 4

Since it is an isoceles triangle the altitude x bisects the base 10. Thus giving you 2 right triangle with a base 5 height x and hypoteneuse 13. Now use the pythagorean theorem. a^2=+^2=c^2
5^2+x^2=13^2
solve for x
the height is 12

Answer 5

If some thing is 40% smaller, you in reality subtract 40%. So 40% of 40 energy is 16: you're trying this by multiplying 40 by 0.4. the answer might want to be 40 - 16 = 24 A shorter way might want to easily be to multiply by 40 by 0.6, for the reason that it truly is a million-0.4.