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baily106
Course Students
 
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Joined: Sat May 03, 2014 1:13 am
 

Official Guide - p. 261, q 11 - parallelogram

by baily106 Sun Jun 08, 2014 7:26 pm

Question 11 on page 261 is another problem for which there is a figure which I cannot draw on here.

The question is how does one determine the perimeter of parallelogram ABCD when AD is 12 and the extended triangle drawn beyond CD has base 2 and height 4?

Thanks,
Anisha
tommywallach
Manhattan Prep Staff
 
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Joined: Thu Mar 31, 2011 11:18 am
 

Re: Official Guide Book Question

by tommywallach Mon Jun 09, 2014 11:23 pm

Hey Anisha,

The definition of a parallelogram is that the two sets of sides are parallel. So we know that that 4 x 2 triangle on the right is also on the left, so the area is just base times height.

Area = base * height = 4 * 12 = 48

For the perimeter, we need to solve the right triangle's hypotenuse using Pythagoras. 4^2 + 2^2 = x^2 --> 16 + 4 = x^2 --> 20 = x^2 --> x=rt. 20 --> x = 2 * rt. 5

Now we know the perimeter is made up of two sides that are 2 * rt. 5 and two sides that are 12, so the perimeter is 24 + 4 rt. 5

Finally for finding the diagonal, draw a line down from point B that meets the base of the parallelogram at a right angle. We know the height of that new right triangle is 4, and the base is 10 (that's because it's 12 - 2, because it's two on the left side just as it's two on the right side).

4 ^ 2 + 10 ^ 2 = x ^ 2 --> 16 + 100 = x ^2 --> x = rt. 116 --> 2 * rt. 29

Hope that helps!

-t