Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.

What is Pythagoras Theorem?

The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.

The formula for Pythagoras Theorem is given by,

$h^{2}=a^{2} +b^{2}$

Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.

Each Subtraction in view of Pythagoras Theorem

It is is given that,

$d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }$

or $d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}$

Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.

Learn more about Pythagoras Theorem here:

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8 0

2 years ago

Please help me with this thanks

geniusboy [140]

When area is equal 1120. We can write an equation
(x+4)(-x+64)=1120
-x²-4x+64x+256=1120
-x²+60x+256-1120=0
-x²+60x-864=0
D=b² - 4ac= 3600-4*864=144, √D=12
x= (-b+/-√D)/2a
x=(-60+/-12)/(-2)
x=24, x=36
For x=24
(x+4)=24+4=28
(-x+64)=(-24+64)=40
For x=36
(x+4)=36+4=40
(x-64) =(-36+64)=28
So sides should be 28 and 40 in.
We did not get any extraneous solutions. They could be if we get negative length side, for example. They can come because a quadratic equation can
give positive and negative numbers because a^2 and (-a)^2 give the same positive number.
We chose to solve this equation using formula for quadratic equations, because this equation has too big numbers to solve it using other methods.

5 0

3 years ago