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Lesson 4: Pythagorean theorem application

# Use Pythagorean theorem to find area of an isosceles triangle

We can find the area of an isosceles triangle using the Pythagorean theorem. Once we recognize the triangle as isosceles, we divide it into congruent right triangles. Then we use the theorem to find the height. Last, we calculate the area with the formula: 1/2 × base × height.

## Want to join the conversation?

• Can you tell me what is the use of Pythagorean in our daily
life?
• Here is an answer from Hadriel Ramos (check the comments!) :Actually it is one of the most fundamental theorems in basic geometry.

Just imagine a tall post (10 meters High) and you are standing 20 meters away. And you wanted to tie a rope to the high point of the post to the ground from which you are standing. You use the Pythagorean Theorem.
• Have a question for right triangle. Need help to solve it.
The hypotenuse of right triangle is 26cm. The sum of two other sides is 34cm. Find the length of two sides.
• Well, we'll start by defining the sides. one unknown side will be x, and one will be 34 - x. Now, the Pythagorean theorem says that x^2 + (34 - x)^2 = 26^2.
Multiplying out, we get:
x^2 + 34^2 + x^2 - 68x = 676
Simplifying:
2x^2 - 68x + 1156 = 676
2x^2 - 68x + 480 = 0
x^2 - 34x + 240 = 0
Now, we have a quadratic equation, which we can factor:
{x^2 - 34x + 240 = 0} = {(x - 24)(x - 10) = 0}
Now we can solve for x by dividing by x - 10:
(x - 24)(x - 10) = 0
x - 24 = 0
And by dividing by x - 24:
x - 10 = 0
So, we have that x = 10, and x = 24. This means that the answer to your problem is [24, 10].
• Can you use the Pythagorean Theorem to solve for any triangle? If so, can you please add an example for a scalene triangle.
• You can work out the area for triangles which are made up with right triangles, like the triangle that Sal uses in this video.
Hope this helps.
• How if the value of the base is missing
• If the value of the base is missing , than you dont use pythagorean theroem for it.
• At , Sal said 100 and 44, not 144. I thought you only use "and" when you are referring to decimals?
• lots of people say 100 and 44 but they mean 144 its probably because of his accent but yes you are really only supposed to use and when you are referring to decimals does that help answer your question?
• i cant describe my loathing for the pethagriam
• then kys
• why are we learning this?