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# If the length, l, of a rectangle is six times the width, w, of the sam

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Math Expert
Joined: 02 Sep 2009
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If the length, l, of a rectangle is six times the width, w, of the sam  [#permalink]

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02 Sep 2018, 22:16
00:00

Difficulty:

15% (low)

Question Stats:

75% (00:53) correct 25% (01:14) wrong based on 38 sessions

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If the length, l, of a rectangle is six times the width, w, of the same rectangle, which of the following is the diagonal of the rectangle in terms of w?

A. $$\sqrt{6}w$$

B. $$\sqrt{7}w$$

C. 7w

D. $$\sqrt{37}w$$

E. 37w

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Re: If the length, l, of a rectangle is six times the width, w, of the sam  [#permalink]

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02 Sep 2018, 22:24
So the
Length- 6w
Width- w

Diagonal d =?

d^2 = (6w)^2 + (w)^2

So D

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Re: If the length, l, of a rectangle is six times the width, w, of the sam  [#permalink]

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03 Sep 2018, 08:18
Length = 6w
Width = w

Using Pythagoras,

(6w)^2 + (w)^2 = d^2
36w^2 + w^2 = d^2
37w^2 = d^2
Hence,
d= [(37)^1/2]w

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Re: If the length, l, of a rectangle is six times the width, w, of the sam  [#permalink]

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07 Sep 2018, 16:10
Bunuel wrote:
If the length, l, of a rectangle is six times the width, w, of the same rectangle, which of the following is the diagonal of the rectangle in terms of w?

A. $$\sqrt{6}w$$

B. $$\sqrt{7}w$$

C. 7w

D. $$\sqrt{37}w$$

E. 37w

The length of the rectangle is 6w, and the width is w. To determine the length of the diagonal, we can use the Pythagorean theorem, and we have:

(6w)^2 + w^2 = d^2

36w^2 + w^2 = d^2

37w^2 = d^2

w√37 = d

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Re: If the length, l, of a rectangle is six times the width, w, of the sam  [#permalink]

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08 Sep 2018, 10:35
Hi All,
here is the mistake I've maid, could you explain me why I was wrong?

I got to the part of writting down the following : w²+(6w)²=d²
So I decided to square root everything and did squrt(w²+(6w)²=d²) --> w+6w=d --> 7w=d

Of course there was a trap answer with 7w (C)

So I understand your reasoning through the 36w but I don't get why I am not allowed to square root everything.

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Re: If the length, l, of a rectangle is six times the width, w, of the sam   [#permalink] 08 Sep 2018, 10:35
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