M10: 31

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 .

Awesome. Thanks very much.

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:



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?

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

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!