M10: 31

Question

If the area of a parallelogram is 100, what is the perimeter of the parallelogram?

1) The base of the parallelogram is 10.
2) One of the angles of the parallelogram is 45 degrees.

Why C and not E?

Am struggling to understand how we can use the pythagorean theorem when we don't know which pair of angles are 45 degrees each in the parallelogram. What am I missing here? Would appreciate some help here.

sid3699 · Answer

Anyone <img src="{SMILIES_PATH}/icon_question.gif" alt=":?:" title="Question" />

hgp2k · Answer

It is not necessary to know which pair of angles is 45 degrees. I have attached an image for your reference. Parallelogram.jpg Please let me know if you want me to explain further

dzyubam · Answer

Hi,

I've drawn a picture to be able to explain the problem better. S1 tells us that AD in the picture below equals 10. If the area of the parallelogram is 100, than its height BD equals \(\frac{100}{10} = 10\). Now, S2 tells us that one of the angles is 45 degrees. We marked \(\angle BAD\) as a 45 degrees angle. So, we have an isosceles triangle ABD with BD equal to AD. We know that angle ADB is the right angle and can find AB using the Pythagorean theorem. It will equal \(\sqrt{20}\), but we don't even have to find the length of the side or calculate the perimeter if we already know we have enough info. You can save some time on these DS question this way.

Did it help? Hope it did

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Attachments

m10-31.png [ 1.83 KiB | Viewed 3469 times ]

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sid3699 · Answer

Awesome. Thanks very much.

cano · Answer

I got this question wrong for a stupid reason (thought "quadrilateral" instead of "parallelogram"). Later it clicked, but it took longer since I got confused reading this piece in the explanation:

Statement (1) by itself is insufficient. We know the base and the height of the parallelogram; however,  the height can equal the side of the parallelogram (in case of a rectangle) or it can exceed it .

Statement (2) by itself is insufficient. Nothing can be established about the length of the base of the parallelogram.

Statements (1) and (2) combined are sufficient. The length of the side can be found by the Pythagorean theorem.
The correct answer is C.

As I read it, it was difficult to visualize the height exceeding a side. Am I reading it correctly? How would you correct the bold part?

seku · Answer

Area of parallelogram = base * height = 100. perimeter = 2 (base + side)

St1: base = 10, so height = 10. side is unknown still. not sufficient

St 2: angle = 45. so the triangle formed by base (part) and height is an isosceles triangle 90-45-45. sqrt(2):1:1. so the height and base part should be equal, but unknown.

Both: from St1 base = 10 and height = 10, through st2 side = 10* sqrt(2). As we know side and base, perimeter could be calculated.

C

nithin · Answer

Why not B?

Since you know that one of the angles is 45 degrees, you can tell that that the parallelogram is made of two 45/45/90 triangles. This would lead you to knowing that the height = the base.

This would lead you to knowing that:

100 = height * base = height * height = base * base

So therefore, height and base must be equal to 10.

And this leads you to knowing that the perimeter must be equal to 20 + 20 * root(2).

Am I missing something or making any leaps of logic that I shouldn't be?

Thanks!

M10: 31

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