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Kiran and Mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner. Mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. Do you agree with either of them?

Respuesta :

sqdancefan

Kiran is correct. (I agree with Kiran.)

_____

Suppose the length and width are L and W. The Pythagorean theorem says the diagonal distance is ...

... d = √(L² +W²)

If the dimensions are doubled, the the diagonal distance becomes ...

... D = √((2L)² +(2W)²) = √(4(L² +W²)) = 2√(L² +W²)

... D = 2d

Answer:

Kiran's statement is correct.

Step-by-step explanation:

Kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner.

Let the original length be = l

Let the original width be = w

Let the original diagonal be = d1

As per Pythagoras theorem,

[tex]d1^{2} =l^{2} +w^{2}[/tex]

When the dimensions are twice the original;

Length = 2l

Width = 2w

Diagonal = d2

We get the formula :

[tex]d2^{2} =2l^{2} +2w^{2}[/tex]

[tex]d2^{2} =2(l^{2} +w^{2})[/tex]

Or [tex]d2^{2} =2d1^{2}[/tex]

So, we can say that Kiran is correct.

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