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Natasha_Volkova [10]
4 years ago
5

Mauro has 140 ft of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the sho

rter piece. What will the length of the longer piece be? _________ ft
Mathematics
2 answers:
ipn [44]4 years ago
4 0
140= x +3x
140 =4x
140/4= 4x/4
35= x
3x= 105
The length of the longer piece is 105 feet

Studentka2010 [4]4 years ago
4 0

Answer:

The length of the longer piece is 35 feet.

Step-by-step explanation:

Let the length of the longer piece is x

Hence, length of the shorter piece is 3x

Now, the length of the rope is 140 ft. Thus, we have the equation

x+3x=140

Add the like terms. x+3x=4x

4x=140

Divide both sides by 4

x=35

Therefore, the length of the longer piece is 35 feet.

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Now add the squares of the numerator and denominator, as in the example.
(2x+2)^2+(x^2+2x)^2= \\ 4x^2+8x+4+x^4+4x^3+4x^2= \\ x^4+4x^3+8x^2+8x+4

So this number has to be a perfect square.
x^4+4x^3+8x^2+8x+4= \\
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x^2(x^2+2x+2)+2x(x^2+2x+2)+2(x^2+2x+2)= \\
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It is a perfect square, so this method always works.

The numbers 2x+2, \ x^2+2x, \ (x^2+2x+2)^2 are a Pythagorean triple for any x \in \mathbb{N^+}.
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Rufina [12.5K]

Step-by-step explanation:

a) The slope formula is given by

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