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### Course: Grade 8 (Virginia)>Unit 6

Lesson 5: Applying the Pythagorean theorem

# Use Pythagorean theorem to find area of an isosceles triangle

Sal uses the Pythagorean theorem to find area of an isosceles triangle.

## 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.
• why are we learning this?
• Every skill that we learn, no matter how insignificant it may seem, will be used someday. Most, if not all, of the lessons here on Khan Academy can help with at least one job where it would be vital to have an understanding of it.
• m
2 = x + 91 how do i find the solution to this eqation with an isosyles triangle that has a degree of 50
• At , Sal said 100 and 44, not 144. I thought you only use "and" when you are referring to decimals?