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BartSMP [9]
2 years ago
10

!30 POINTS! How can I use this trapezoid to prove the Pythagorean Theorem?

Mathematics
1 answer:
stiks02 [169]2 years ago
6 0

Answer:

Pythagorean Theorem: c2 = a2 + b2

Find the area by adding the areas of the three triangles. The area of a right triangle is: A = ½bh

Two triangles are identical so you can just multiply the area of the first triangle by two: 2A1 = 2(½bh) = 2(½ab) = ab.

The total area of the trapezoid is : A1 + A2 = ab + ½c2

You multiply both sides by 2 to get rid of the ½: (a2 + 2ab + b2) = 2ab + c2

You subtract out the 2ab: a2 + b2 = c2.

Then what is left is the proof: a2 + b2 = c2

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a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream
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the coordinates where the bridges must be built is (3,-6) and (6,3) .

<u>Step-by-step explanation:</u>

Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:

Basically we need to find values of x for which f(x) = g(x) :

⇒ f(x)-g(x)=0

⇒ 3x^2- 24x + 39-(3x - 15 ) =0

⇒ 3x^2- 24x + 39-3x + 15  =0

⇒ 3x^2- 27x + 54  =0

⇒ x^2- 9x + 18  =0

⇒ x^2- 6x-3x + 18  =0

⇒ x(x- 6)-3(x - 6)  =0

⇒ (x-3)(x- 6)  =0

⇒ x=3 , x=6

Value of g(x) at x = 3 : y=3x -15 = 3(3)-15 = -6

Value of g(x) at x = 6 : y=3x -15 = 3(6)-15 = 3

Therefore , the coordinates where the bridges must be built is (3,-6) and (6,3) .

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So, there can be a maximum of 6 members in the club.. 

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