Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
<h3>What is the Pythagoras Theorem?</h3>
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In △ABD and △ACB,
∠A = ∠A (common)
∠ADB = ∠ABC (both are right angles)
Thus, △ABD ∼ △ACB (by AA similarity criterion)
Similarly, we can prove △BCD ∼ △ACB.
Thus △ABD ∼ △ACB,
Therefore, AD/AB = AB/AC.
We can say that AD × AC = AB².
Similarly, △BCD ∼ △ACB.
Therefore,
CD/BC = BC/AC.
We can also say that
CD × AC = BC².
Adding these 2 equations, we get
AB² + BC² = (AD × AC) + (CD × AC)
AB² + BC² =AC(AD +DC)
AB² + BC² = AC²
Hence proved
Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
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Answer:
6. X= 121
7. x= 18
8. X= 7
9. x= 31
Step-by-step explanation: do u need the steps?
I don’t know what you’re tying to say
Answer:
144 ways
Step-by-step explanation:
Let's think of the 3 persons sitting together as "one". So essentially we have 3 + "1" = "4" persons to arrange.
THey can be arranged in 4! ways, which is:
4! = 4 * 3 * 2 * 1 = 24 ways
Now, the 3 persons themselves can be arranged in 3! ways, which is:
3! = 3 * 2 * 1 = 6 ways
Total ways = 4! * 3! = 24 * 6 = 144 ways
