SOLUTION: I am really having trouble getting the pythagorean theorem to find a height of a triangle. One of the sides is thirteen and the base is 12. After that they wanted me to use that

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Question 29766: I am really having trouble getting the pythagorean theorem to find a height of a triangle. One of the sides is thirteen and the base is 12. After that they wanted me to use that to fine the area. Please help me.
Found 2 solutions by askmemath, josmiceli:
Answer by askmemath(368) (Show Source):
You can put this solution on YOUR website!
Let the sides = 13,12 , X
According to Pythagoras' Theorem
Square of Hypotenuse = Sum of Square of other 2 sides
i.e.

Subtracting 144 on both sides
X = 5
Now
= = 30SqUnits

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Think of it this way
Lean a 13 ft ladder against a building 12 feet away from the building
It won't reach very high up the building, will it?
Pythagoras's theorem says "The square ON the hypotenuse (longest side
equals the sum of the squares ON the other two sides"
That's the way it's often shown-with squares drawn right on the legs of the triangle.
is how you show that with algebra
h is the longest side (it's the length of the ladder) so c = 13
let a = 12

subtract 12^2 from both sides

take the square root of both sides

so the ladder will reach 5 ft up the wall if it's 12 feet away
The area of any triangle is

that's one-half the base times the height)